* Bug #6307 fixed - CACSD: make easy version of lqr, lqe, lqg 11/19011/6
serge.steer [Thu, 26 May 2016 08:45:51 +0000 (10:45 +0200)]
 * Wish 6307 fix + help revisited + unit tests added
 * lftpss bug fix (PID demo)

Change-Id: I0b158e0817ee84aa786dd1caad86caab9d3db430

227 files changed:
scilab/CHANGES.md
scilab/modules/cacsd/help/en_US/control_design/control_loop/lft.xml
scilab/modules/cacsd/help/en_US/control_design/linear_quadratic/lqe.xml
scilab/modules/cacsd/help/en_US/control_design/linear_quadratic/lqg.xml
scilab/modules/cacsd/help/en_US/control_design/linear_quadratic/lqi.xml [new file with mode: 0644]
scilab/modules/cacsd/help/en_US/control_design/linear_quadratic/lqr.xml
scilab/modules/cacsd/help/fr_FR/control_design/control_loop/augment.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/control_loop/feedback.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/control_loop/lft.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/disturbance_decoupling/ddp.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/ccontrg.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/dhinf.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/dhnorm.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/gamitg.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h2norm.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_cl.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_inf.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_inf_st.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_norm.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/hinf.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/linf.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/linfn.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/macglov.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/nehari.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/parrot.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/fourplan.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/gcare.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/gfare.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/leqr.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqe.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg2stan.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg_ltr.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqr.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/kpure.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/krac2.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/ppol.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/stabil.xml [deleted file]
scilab/modules/cacsd/help/fr_FR/control_design/tracking/gfrancis.xml [deleted file]
scilab/modules/cacsd/help/images/lft.png [new file with mode: 0644]
scilab/modules/cacsd/help/images/lqg.png [new file with mode: 0644]
scilab/modules/cacsd/help/images/lqgi.png [new file with mode: 0644]
scilab/modules/cacsd/help/images/lqi.png [new file with mode: 0644]
scilab/modules/cacsd/help/images/lqifull.png [new file with mode: 0644]
scilab/modules/cacsd/help/images/twoMasses.png [new file with mode: 0644]
scilab/modules/cacsd/help/pt_BR/control_design/control_loop/augment.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/control_loop/feedback.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/control_loop/lft.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/disturbance_decoupling/ddp.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/ccontrg.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/dhinf.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/dhnorm.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/gamitg.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/h2norm.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/h_cl.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/h_inf.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/h_inf_st.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/h_norm.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/hinf.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/linf.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/linfn.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/macglov.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/nehari.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/parrot.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/fourplan.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/gcare.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/gfare.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/leqr.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/lqe.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/lqg.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/lqg2stan.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/lqg_ltr.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/linear_quadratic/lqr.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/pole_placement/kpure.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/pole_placement/krac2.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/pole_placement/ppol.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/pole_placement/stabil.xml [deleted file]
scilab/modules/cacsd/help/pt_BR/control_design/tracking/gfrancis.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/control_loop/augment.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/control_loop/feedback.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/control_loop/lft.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/disturbance_decoupling/ddp.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/ccontrg.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/dhinf.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/dhnorm.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/gamitg.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/h2norm.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/h_cl.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/h_inf.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/h_inf_st.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/h_norm.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/hinf.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/linf.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/linfn.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/macglov.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/nehari.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/h_infinity/parrot.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/fourplan.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/gcare.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/gfare.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/leqr.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/lqe.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/lqg.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/lqg2stan.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/lqg_ltr.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/linear_quadratic/lqr.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/pole_placement/kpure.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/pole_placement/krac2.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/pole_placement/ppol.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/pole_placement/stabil.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/control_design/tracking/gfrancis.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/noisegen.xml [deleted file]
scilab/modules/cacsd/help/ru_RU/prbs_a.xml [deleted file]
scilab/modules/cacsd/macros/lft.sci
scilab/modules/cacsd/macros/lqe.sci
scilab/modules/cacsd/macros/lqg.sci
scilab/modules/cacsd/macros/lqi.sci [new file with mode: 0644]
scilab/modules/cacsd/macros/lqr.sci
scilab/modules/cacsd/macros/smga.sci
scilab/modules/cacsd/tests/unit_tests/lft.dia.ref [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lft.tst [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqe.dia.ref [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqe.tst [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqg.dia.ref [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqg.tst [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqi.dia.ref [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqi.tst [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqr.dia.ref [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/lqr.tst [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/plzr.dia.ref
scilab/modules/cacsd/tests/unit_tests/plzr.tst
scilab/modules/helptools/etc/images_md5.txt
scilab/modules/helptools/images/_LaTeX_lft.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lft.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_10.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_11.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_12.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_13.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_14.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_15.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_16.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_17.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_18.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_19.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_20.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_21.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_22.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_23.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_24.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_25.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_26.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_27.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_28.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_29.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_3.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_30.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_31.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_32.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_33.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_34.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_35.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_36.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_37.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_4.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_5.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_6.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_7.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_8.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqe.xml_9.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_10.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_11.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_12.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_13.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_3.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_4.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_5.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_6.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_7.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_8.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqg.xml_9.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_3.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_4.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_5.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_6.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_7.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqi.xml_8.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_1.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_10.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_11.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_12.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_13.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_14.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_15.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_16.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_17.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_18.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_19.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_2.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_20.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_21.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_22.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_23.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_24.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_3.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_4.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_5.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_6.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_7.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_8.png [new file with mode: 0644]
scilab/modules/helptools/images/_LaTeX_lqr.xml_9.png [new file with mode: 0644]
scilab/modules/helptools/images/lft.png [new file with mode: 0644]
scilab/modules/helptools/images/lqe_1.png [new file with mode: 0644]
scilab/modules/helptools/images/lqg.png [new file with mode: 0644]
scilab/modules/helptools/images/lqg_2.png [new file with mode: 0644]
scilab/modules/helptools/images/lqgi.png [new file with mode: 0644]
scilab/modules/helptools/images/lqi.png [new file with mode: 0644]
scilab/modules/helptools/images/lqifull.png [new file with mode: 0644]
scilab/modules/helptools/images/lqr_1.png [new file with mode: 0644]
scilab/modules/helptools/images/twoMasses.png [new file with mode: 0644]
scilab/modules/overloading/macros/%r_m_s.sci
scilab/modules/polynomials/macros/invr.sci

index 9d5342c..b11e1db 100644 (file)
@@ -205,6 +205,8 @@ or a 3-components vector to set the position in axes coordinates to draw the dat
 * The zero-pole-gain (zpk) representation added for linear dynamical systems.
 * It is now possible to add a title to the axes via the "Label -> Title" context menu entry
 * `getPreferencesValue` can now read a tag having multiple occurrences, and accepts the path to a preferences file instead of its XML handle.
+* atomsSetConfig does not update cache.
+* lqi function added to compute "linear quadratic integral compensator".
 
 
 Help pages:
@@ -342,6 +344,7 @@ Bug Fixes
 * [#2919](http://bugzilla.scilab.org/show_bug.cgi?id=2919): The `fchamp` example and demo were unclear and badly rendered
 * [#4327](http://bugzilla.scilab.org/show_bug.cgi?id=4327): Overloading did not support custom types names longer than 8 characters
 * [#5723](http://bugzilla.scilab.org/show_bug.cgi?id=5723): Cross-references were missing between axis_properties and axes_properties help pages
+* [#6307](http://bugzilla.scilab.org/show_bug.cgi?id=6307): Make easy version of lqr, lqe, lqg
 * [#7192](http://bugzilla.scilab.org/show_bug.cgi?id=7192): From S=[], S($+1,:) = some_row inserted it in row#2 after a parasitic row#1.
 * [#7649](http://bugzilla.scilab.org/show_bug.cgi?id=7649): `isempty` returned `%F` on `struct()`, `{}` or `list(,)` and was not shortcut
 * [#7696](http://bugzilla.scilab.org/show_bug.cgi?id=7696): The `parallel_run` help page was poorly formated
index 9f8b186..0cbbcc2 100644 (file)
@@ -20,9 +20,8 @@
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>[P1]=lft(P,K)
-            [P1]=lft(P,r,K)
-            [P1,r1]=lft(P,r,Ps,rs)
+        <synopsis>S=lft(P,R)
+            [S,s]=lft(P,p,R [,r])
         </synopsis>
     </refsynopsisdiv>
     <refsection>
                 <term>P</term>
                 <listitem>
                     <para>
-                        linear system (<literal>syslin</literal> list), the ``augmented'' plant, implicitly partitioned into four blocks (two input ports and two output ports).
+                        linear system (in state space or transfer
+                        function representation) or a simple gain, the
+                        ``augmented'' plant, implicitly partitioned
+                        into four blocks (two input ports and two
+                        output ports).
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>K</term>
+                <term>p</term>
                 <listitem>
                     <para>
-                        linear system (<literal>syslin</literal> list), the controller (possibly an ordinary gain).
+                        1x2 row vector,  the  dimensions of the <literal>P_22</literal> block (see below).
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>R</term>
+                <listitem>
+                    <para>
+                        llinear system (in state space or transfer
+                        function representation) or a simple gain,
+                        implicitly partitioned into four blocks (two
+                        input ports and two output ports).
                     </para>
                 </listitem>
             </varlistentry>
                 <term>r</term>
                 <listitem>
                     <para>
-                        1x2 row vector, dimension of <literal>P22</literal>
+                        1x2 row vector, dimension of the
+                        <literal>R_22</literal> block . This argument should  not
+                        be used. It is retained for compatibility with
+                        previous versions.
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>Ps  </term>
+                <term>S</term>
                 <listitem>
                     <para>
-                        linear system (<literal>syslin</literal> list), implicitly partitioned into four blocks (two input ports and two output ports).
+                        linear system, the linear fractional transform.
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>rs  </term>
+                <term>s</term>
                 <listitem>
                     <para>
-                        1x2 row vector, dimension of <literal>Ps22</literal>
+                        1x2 row vector, dimension of the <literal>S_22</literal> block (see below).
                     </para>
                 </listitem>
             </varlistentry>
         <title>Description</title>
         <para>
             Linear fractional transform between two standard plants
-            <literal>P</literal> and <literal>Ps</literal> in state space form or in
-            transfer form (<literal>syslin</literal> lists).
-        </para>
-        <para>
-            <literal>r= size(P22) rs=size(P22s)</literal>
-        </para>
-        <para>
-            <literal>lft(P,r, K)</literal> is the linear fractional transform
-            between <literal>P</literal> and a controller <literal>K</literal>
-            (<literal>K</literal> may be a gain or a controller in state space form
-            or in transfer form);
-        </para>
-        <para>
-            <literal>lft(P,K)</literal> is <literal>lft(P,r,K)</literal> with
-            <literal>r</literal>=size of <literal>K</literal> transpose;
-        </para>
-        <para>
-            <literal>P1= P11+P12*K* (I-P22*K)^-1 *P21</literal>
+            in state space form or in transfer form:
         </para>
         <para>
-            <literal>[P1,r1]=lft(P,r,Ps,rs)</literal> returns the generalized (2
-            ports) lft of <literal>P</literal> and <literal>Ps</literal>.
-        </para>
-        <para>
-            <literal>P1</literal> is the pair two-port interconnected plant and the
-            partition of <literal>P1</literal> into 4 blocks in given by
-            <literal>r1</literal> which is the dimension of the <literal>22</literal>
-            block of <literal>P1</literal>.
+            <mediaobject>
+                <imageobject>
+                    <imagedata fileref="../../../images/lft.png"/>
+                </imageobject>
+            </mediaobject>
         </para>
+        <variablelist>
+            <varlistentry>
+                <term>
+                    Syntax  <literal>S=lft(P,R)</literal>
+                </term>
+                <listitem>
+                    <para>
+                        Computes the linear fractional transform between the
+                        systems <literal>P</literal> and a controller
+                        <literal>R</literal>. The system <literal>S</literal> corresponds to the transfer <latex>z=\text{ S } w</latex>
+                    </para>
+                    <para>
+                        if <literal>ny</literal> and <literal>nu</literal> are
+                        respectively the number of inputs and outputs of
+                        <literal>R </literal>, one must have
+                        <literal>size(P)>=[ny nu]</literal>.
+
+                        The system returned is formally equivalent to
+                        <programlisting><![CDATA[
+                i1 = 1:($-ny);j1=1:($-nu);
+                i2 = ($-ny+1):$;j1=($-nu+1):$;
+                S = P(i1,j1) + P(i1,j2) * R * (eye() - P(i2,j2) * R) \P(i2,j1)
+                ]]>
+                        </programlisting>
+                        Using <literal>lft</literal> instead of the code above avoids numerical problems and non
+                        minimal realization.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>
+                    Syntax  <literal>[S,s]=lft(P,p,R)</literal>
+                </term>
+                <listitem>
+                    <para>
+                        with <literal>p= [ny,nu]</literal>  Forms the
+                        generalized (2 ports) lft of <literal>P</literal> and
+                        <literal>R</literal>.
+                    </para>
+                    <para>
+                        <literal>S</literal> is the two-port interconnected
+                        plant, which correspond to the transfer: <latex
+              style="display">\left[
+                            \begin{array}{l}z_1\\z_2\end{array}\right]=\text{ S } \left[
+                            \begin{array}{l}w_1\\w_2\end{array}\right]
+                        </latex>
+                        <literal>s</literal> is the dimension of the
+                        <literal>22</literal> block of <literal>S</literal>.
+                    </para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
         <para>
             <literal>P</literal> and <literal>R</literal> can be PSSDs i.e. may admit a
             polynomial <literal>D</literal> matrix.
     <refsection>
         <title>Examples</title>
         <programlisting role="example"><![CDATA[
-s=poly(0,'s');
-P=[1/s, 1/(s+1); 1/(s+2),2/s]; K= 1/(s-1);
-lft(P,K)
-lft(P,[1,1],K)
-P(1,1)+P(1,2)*K*inv(1-P(2,2)*K)*P(2,1)   //Numerically dangerous!
-ss2tf(lft(tf2ss(P),tf2ss(K)))
+//simple feeback case
+
+P=[1/%s, 1/(%s+1); 1/(%s+2),2/%s];
+R= 1/(%s-1);
+lft(P,R)
+
+P(1,1)+P(1,2)*R*inv(1-P(2,2)*R)*P(2,1)   //Numerically dangerous!
+
 lft(P,-1)
-f=[0,0;0,1];w=P/.f; w(1,1)
-//Improper plant (PID control)
-W=[1,1;1,1/(s^2+0.1*s)];K=1+1/s+s
-lft(W,[1,1],K); ss2tf(lft(tf2ss(W),[1,1],tf2ss(K)))
+
+//Improper systems
+W=[1,1;1,1/(%s^2+0.1*%s)];
+K=tf2ss(1+1/%s+%s);////Improper (PID control)
+lft(W,[1,1],K)
  ]]></programlisting>
     </refsection>
+    <refsection>
+        <title>References</title>
+        <ulink
+      url="http://www.cds.caltech.edu/~doyle/wiki/images/7/70/CDC1991.pdf">"Review
+            of LFTs, LMIs, and μ",John Doyle, Andy Packard and Kemin Zhou, CDC december 1991
+        </ulink>
+    </refsection>
     <refsection role="see also">
         <title>See also</title>
         <simplelist type="inline">
@@ -142,3 +201,4 @@ lft(W,[1,1],K); ss2tf(lft(tf2ss(W),[1,1],tf2ss(K)))
         </simplelist>
     </refsection>
 </refentry>
+<!--http://www.cds.caltech.edu/~doyle/wiki/images/7/70/CDC1991.pdf-->
index 3889867..4a6ffca 100644 (file)
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>[K,X]=lqe(P21)</synopsis>
+        <synopsis>[K,X]=lqe(Pw)</synopsis>
+        <synopsis>[K,X]=lqe(P,Qww,Rvv [,Swv])</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
         <variablelist>
             <varlistentry>
-                <term>P21</term>
+                <term>Pw</term>
                 <listitem>
                     <para>
-                        <literal>syslin</literal> list
+                        A state space representation of a linear
+                        dynamical system (see <link
+                        linkend="syslin">syslin</link>)
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>K, X</term>
+                <term>P</term>
                 <listitem>
-                    <para>real matrices</para>
+                    <para>
+                        A state space representation of a linear
+                        dynamical system (<literal>nu</literal> inputs,
+                        <literal>ny</literal> outputs,
+                        <literal>nx</literal> states) (see <link
+                      linkend="syslin">syslin</link>)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Qww</term>
+                <listitem>
+                    <para>
+                        Real <literal>nx</literal> by
+                        <literal>nx</literal> symmetric matrix, the
+                        process noise variance
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Rvv</term>
+                <listitem>
+                    <para>
+                        full rank real <literal>ny</literal> by
+                        <literal>ny</literal> symmetric matrix, the
+                        measurement noise variance.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Swv</term>
+                <listitem>
+                    <para>
+                        real <literal>nx</literal> by
+                        <literal>ny</literal> matrix, the process
+                        noise vs measurement noise covariance. The
+                        default value is zeros(nx,ny).
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>K</term>
+                <listitem>
+                    <para>a real matrix, the optimal gain.</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>a real symmetric matrix, the stabilizing solution of the Riccati equation.</para>
                 </listitem>
             </varlistentry>
         </variablelist>
     <refsection>
         <title>Description</title>
         <para>
-            <literal>lqe</literal> returns the Kalman gain for the filtering
-            problem in continuous or discrete time.
+            This function computes the linear optimal LQ estimator gain of
+            the state estimator for a detectable (see <link
+        linkend="dt_ility">dt_ility</link>) linear dynamical system and
+            the variance matrices for the process and the measurement
+            noises.
+        </para>
+        <refsection>
+            <title>
+                Syntax <literal>[K,X]=lqe(P,Qww,Rvv [,Swv])</literal>
+            </title>
+            <para>
+                Computes the linear optimal LQ estimator gain K for the
+                dynamical system:
+                <latex style="display"
+          align="left"><![CDATA[\text{P}=\left\lbrace \begin{array}{l}\dot{x}=A x+B
+          u+w\\y=C x+D u +v\end{array}\right. \text{ in continuous time}]]></latex>
+            </para>
+            or
+            <para>
+                <latex style="display"
+          align="left"><![CDATA[\text{P}=\left\lbrace \begin{array}{l}x^+=A x+B u
+          +w\\y=C x+D u +v\end{array}\right. \text{ in discrete time}]]></latex>
+            </para>
+            <para>
+                Where <latex>w \text{ and } v</latex> are white noises such
+                as <latex>\mathbb{E}(w w')=Q_{ww} \text{ , }\mathbb{E}(v
+                    v')=R_{vv} \text{ and }\mathbb{E}w v')=S_{wv}
+                </latex>
+            </para>
+            <note>
+                <title>Caution</title>
+                <para>
+                    The values of <latex>B</latex> and <latex>D</latex>
+                    are not taken into account.
+                </para>
+            </note>
+            <note>
+                <title>Standard form</title>
+                <para>
+                    <latex style="display"
+           align="left"><![CDATA[\mathbb{E}\left(\left[\begin{array}{l}w\\v\end{array}\right]\left[\begin{array}{ll}w'&v'\end{array}\right]\right)=\left[\begin{array}{ll}Q_{ww}&S_{wv}\\S_{wv}'&R_{vv}\end{array}\right]]]></latex>
+           This covariance matrix can be factored using full-rank
+           factorization (see <link linkend="fullrf">fuffrf</link>) as
+           <latex style="display"
+           align="left"><![CDATA[\left[\begin{array}{l}B_w\\D_w\end{array}\right]
+           \left[\begin{array}{ll}B_w'&D_w'\end{array}\right]]]></latex>
+
+           And consequently the initial dynamical system is equivalent to
+
+           <latex style="display"
+           align="left">\left\{\begin{array}{l}\dot{x}=A x+B u +B_w w
+           \\y=C x+D u+D_w w\end{array}\right. \text{ in continuous time }
+           </latex>
+           or
+           <latex style="display"
+                  align="left">\left\{\begin{array}{l}x^+=A x+B u+B_w
+           w\\y=C x+D u+D_w w \end{array}\right. \text{ in discrete time.}</latex>
+
+           Where <latex>w</latex> is now a white noise such
+           as <latex>\mathbb{E}(w w')=I</latex>
+        </para>
+        </note>
+      </refsection>
+
+      <refsection>
+        <title>Syntax <literal>[K,X]=lqe(Pw)</literal></title>
+        <para>
+          Computes the linear optimal LQ estimator  gain K  for the dynamical system
+
+          <latex style="display"
+          align="left">\text{Pw}=\left\{\begin{array}{l}\dot{x}=A
+          x+B_w w\\z=C x+D_w w\end{array}\right. \text{ in continuous time or }\text{Pw}=\left\{\begin{array}{l}x^+=A
+          x+B_w w\\z=C x+D_w w\end{array}\right. \text{ in discrete time.}</latex>
         </para>
         <para>
-            <literal>P21</literal> is a <literal>syslin</literal> list representing the system <literal>P21=[A,B1,C2,D21] P21=syslin('c',A,B1,C2,D21) or P21=syslin('d',A,B1,C2,D21)</literal>
+          Where <latex>w</latex> is a white noise with unit covariance.
         </para>
+      </refsection>
+      <refsection>
+      <title>Properties</title>
+      <itemizedlist>
+        <listitem>
         <para>
-            The input to <literal>P21</literal> is a white noise with variance:
+           <latex>A+K C</latex> is stable.
         </para>
-        <programlisting role=""><![CDATA[
-     [B1 ]               [Q  S]
-BigV=[   ] [ B1' D21'] = [    ]
-     [D21]               [S' R]
- ]]></programlisting>
+        </listitem>
+        <listitem>
         <para>
-            <literal>X</literal> is the solution of the stabilizing Riccati
-            equation and <literal>A+K*C2</literal> is stable.
+          the state estimator is given by the dynamical system:
+
+          <latex style="display" align="left">\dot{\hat{x}}=(A+K
+          C)\hat{x}+(B_w+K D_w) u -K y \text{ in continuous time }</latex>
+
+          <para>or </para>
+          <latex style="display"
+          align="left">\hat{x}^+=(A+K C)\hat{x}+(B_w+K D_w) u -K y \text{
+          in discrete time.}</latex>
+          It minimizes the covariance of the steady state error
+          <latex>x-\hat{x}</latex>.
         </para>
+        </listitem>
+        <listitem>
         <para>
-            In continuous time:
+          For discrete time systems  the state estimator is such that:
+          <latex>\hat{x}_{k+1}= \mathbb{E}(x_k| y_0,...,y_k)</latex> (one-step predicted <latex>x</latex>).
         </para>
-        <programlisting role=""><![CDATA[
-(A-S*inv(R)*C2)*X+X*(A-S*inv(R)*C2)'-X*C2'*inv(R)*C2*X+Q-S*inv(R)*S'=0
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-(X*C2'+S)*inv(R)
- ]]></programlisting>
+        </listitem>
+      </itemizedlist>
+      </refsection>
+       <refsection>
+      <title>Algorithm</title>
+      <para>
+        let <latex>Q=B_w B_w'</latex>, <latex>R=D_w D_w'</latex> and  <latex>S=B_w D_w'</latex>
+      </para>
+      <itemizedlist>
+        <listitem>
         <para>
-            In discrete time:
+          For the continuous time case K is given by
+          <latex style="display"  align="left">K=-(X C'+S) R^{-1} </latex>
         </para>
-        <programlisting role=""><![CDATA[
-X=A*X*A'-(A*X*C2'+B1*D21')*pinv(C2*X*C2'+D21*D21')*(C2*X*A'+D21*B1')+B1*B1'
- ]]></programlisting>
         <para>
-            <literal>K=-(A*X*C2'+B1*D21')*pinv(C2*X*C2'+D21*D21')</literal>
+          where <literal>X</literal> is the solution of the
+          stabilizing Riccati equation
+
+          <latex style="display" align="left">(A-S R^{-1} C) X+X (A-S
+          R^{-1} C)'-X C' R^{-1} C X+Q-S R^{-1} S'=0 </latex>
         </para>
+        </listitem>
+        <listitem>
         <para>
-            <literal>xhat(t+1)= E(x(t+1)| y(0),...,y(t))</literal> (one-step predicted <literal>x</literal>)
-            satisfies the recursion:
+          For the discrete time case K is given by
+          <latex style="display"  align="left">K=-(A X C'+S) (C X C'+R)^+</latex>
+        </para>
+        <para>where <literal>X</literal> is the solution of the stabilizing Riccati equation
+
+          <latex style="display" align="left">A X A'-X-(A X C'+S) (C X
+          C'+R)^+ (C X A'+S')+Q </latex>
         </para>
-        <programlisting role=""><![CDATA[
-xhat(t+1)=(A+K*C2)*xhat(t) - K*y(t).
- ]]></programlisting>
+        </listitem>
+      </itemizedlist>
+     </refsection>
     </refsection>
     <refsection>
         <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-//Assume the equations
-//.
-//x = Ax + Ge
-//y = Cx + v
-//with
-//E ee' = Q_e,    Evv' = R,    Eev' = N
-//
-//This is equivalent to
-//.
-//x = Ax  + B1 w
-//y = C2x + D21 w
-//with E { [Ge ]  [Ge v]' } = E { [B1w ] [B1w D21w]' } = bigR =
-//         [ v ]                  [D21w]
-//
-//[B1*B1'  B1*D21';
-// D21*B1'  D21*D21']
-//=
-//[G*Q_e*G' G*N;
-// N*G' R]
-
-//To find (B1,D21) given (G,Q_e,R,N) form bigR =[G*Q_e*G' G*N;N'*G' R].
-//Then [W,Wt]=fullrf(bigR);  B1=W(1:size(G,1),:);
-//D21=W(($+1-size(C2,1)):$,:)
-//
-//P21=syslin('c',A,B1,C2,D21);
-//[K,X]=lqe(P21);
-
-//Example:
-nx=5;ne=2;ny=3;
-A=-diag(1:nx);G=ones(nx,ne);
-C=ones(ny,nx); Q_e(ne,ne)=1; R=diag(1:ny); N=zeros(ne,ny);
-bigR =[G*Q_e*G' G*N;N'*G' R];
-[W,Wt]=fullrf(bigR);B1=W(1:size(G,1),:);
-D21=W(($+1-size(C,1)):$,:);
-C2=C;
-P21=syslin('c',A,B1,C2,D21);
-[K,X]=lqe(P21);
-//Riccati check:
-S=G*N;Q=B1*B1';
-(A-S*inv(R)*C2)*X+X*(A-S*inv(R)*C2)'-X*C2'*inv(R)*C2*X+Q-S*inv(R)*S'
-
-//Stability check:
-spec(A+K*C)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqr">lqr</link>
-            </member>
-            <member>
-                <link linkend="observer">observer</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
+        <para>
+          Assume the dynamical system formed by two masses connected by a spring and a damper:
+
+          <mediaobject>
+            <imageobject>
+              <imagedata fileref="../../../images/twoMasses.png"/>
+            </imageobject>
+          </mediaobject>
+
+          A force <latex> u=\bar{u}+e</latex> (where <latex>e</latex> is a noise) is applied to the big one, the deviations from  equilibrium positions <latex>dy_1</latex> and <latex>dy_2</latex> of the masses are measured. These measures are also subject to an additionnal noise <latex>v</latex>.
+        </para>
+        <para>
+          A continuous time state space representation of this system is:
+          <latex style="display" align="left"><![CDATA[\left\lbrace\begin{array}{l}
+          \dot{x}=\left[\begin{array}{llll}0&1&0&0\\ -k/M&-b/M&k/M&b/M\\ 0&0&0&1\\ k/m&b/m&-k/m&-b/m \end{array}\right] x +\left[\begin{array}{l}0\\ 1/M\\ 0\\ 0 \end{array}\right] (\bar{u}+e)\\
+          \left[\begin{array}{l}dy_1\\ dy_2\end{array}\right]=\left[\begin{array}{llll}1&0&0&0\\ 0&0&1&0 \end{array}\right] x +v
+          \end{array}\right.]]></latex>
+                    <latex style="display"  align="left">\text{Where }x=\left[\begin{array}{l}dy_1\\ \dot{dy_1}\\ dy_2\\ \dot{dy_2}\end{array}\right]</latex>
+                    and <latex>e</latex> and  <latex>v</latex> are discrete time white noises such as
+                    <latex style="display"  align="left">\mathbb{E}(e e')=Q_e \text{ , }\mathbb{E}(v v')=R_vv \text{ and }\mathbb{E}(e v')=S_{ev} </latex>
+                </para>
+                <para>
+                    The instructions below can be used  to compute a LQ state observer of the discretized version of this dynamical system.
+                </para>
+                <programlisting role="example"><![CDATA[
+// Form the state space model
+M = 1; m = 0.2; k = 0.1; b = 0.004;
+A = [  0     1    0    0
+      -k/M  -b/M  k/M  b/M
+       0     0    0    1
+      k/m  b/m  -k/m  -b/m];
+B = [0; 1/M; 0; 0];
+C = [1 0 0 0  //dy1
+     0 0 1 0];//dy2
+//inputs u and e; outputs dy1 and dy2
+P = syslin("c",A, B, C);
+// Discretize it
+dt=0.5;
+Pd=dscr(P, dt);
+
+//  Set the noise covariance matrices
+Q_e=0.01; //additive input noise variance
+R_vv=0.001*eye(2,2); //measurement noise variance
+Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
+
+//----syntax [K,X]=lqe(P,Qww,Rvv [,Swv])---
+Ko=lqe(Pd,Q_ww,R_vv); //observer gain
+
+//----syntax [K,X]=lqe(P21)---
+bigR =sysdiag(Q_ww, R_vv);
+[W,Wt]=fullrf(bigR);
+Bw=W(1:size(Pd.B,1),:);
+Dw=W(($+1-size(Pd.C,1)):$,:);
+Pw=syslin(Pd.dt,Pd.A,Bw,Pd.C,Dw);
+Ko1=lqe(Pw); //same observer gain
+
+//Check gains equality
+norm(Ko-Ko1,1)
+
+// Form the observer
+O=observer(Pd,Ko);
+//check stability
+and(abs(spec(O.A))<1)
+// Check by simulation
+// Modify Pd to make it return the state
+Pdx=Pd;Pdx.C=eye(4,4);Pdx.D=zeros(4,1);
+t=0:dt:30;
+u=zeros(t);
+x=flts(u,Pdx,[1;0;0;0]);//state evolution
+y=Pd.C*x;
+// simulate the observer
+x_hat=flts([u+0.01*rand(u);y+0.0001*rand(y)],O);
+clf;
+subplot(2,2,1)
+  plot2d(t',[x(1,:);x_hat(1,:)]'),
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_1=dy_1$', '$\hat{x_1}$');L.font_size=3;
+  xlabel('Time (s)')
+subplot(2,2,2)
+  plot2d(t',[x(2,:);x_hat(2,:)]')
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_2=dy_1^+$', '$\hat{x_2}$');L.font_size=3;
+  xlabel('Time (s)')
+subplot(2,2,3)
+  plot2d(t',[x(3,:);x_hat(3,:)]')
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_3=dy_2$', '$\hat{x_3}$');L.font_size=3;
+  xlabel('Time (s)')
+subplot(2,2,4)
+  plot2d(t',[x(4,:);x_hat(4,:)]')
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_4=dy_2^+$', '$\hat{x_4}$');L.font_size=3;
+  xlabel('Time (s)')
+]]></programlisting>
+                <scilab:image>  <![CDATA[
+// Form the state space model
+M = 1; m = 0.2; k = 0.1; b = 0.004;
+A = [  0     1    0    0
+      -k/m  -b/m  k/m  b/m
+       0     0    0    1
+      k/M  b/M  -k/M  -b/M];
+B = [0; 0; 0; 1/M];
+C = [1 0 0 0  //dy1
+     0 0 1 0];//dy2
+//inputs u and e; outputs dy1 and dy2
+P = syslin("c",A, B, C);
+// Discretize it
+dt=0.5;
+Pd=dscr(P, dt);
+
+//  Set the noise covariance matrices
+Q_e=0.01; //additive input noise variance
+R_vv=0.001*eye(2,2); //measurement noise variance
+Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
+
+//----syntax [K,X]=lqe(P,Qww,Rvv [,Swv])---
+Ko=lqe(Pd,Q_ww,R_vv); //observer gain
+
+//----syntax [K,X]=lqe(P21)---
+bigR =sysdiag(Q_ww, R_vv);
+[W,Wt]=fullrf(bigR);
+Bw=W(1:size(Pd.B,1),:);
+Dw=W(($+1-size(Pd.C,1)):$,:);
+Pw=syslin(Pd.dt,Pd.A,Bw,Pd.C,Dw);
+Ko1=lqe(Pw); //same observer gain
+
+//Check gains equality
+norm(Ko-Ko1,1)
+
+// Form the observer
+O=observer(Pd,Ko);
+//check stability
+and(abs(spec(O.A))<1)
+// Check by simulation
+// Modify Pd to make it return the state
+Pdx=Pd;Pdx.C=eye(4,4);Pdx.D=zeros(4,1);
+t=0:dt:30;
+u=zeros(t);
+x=flts(u,Pdx,[1;0;0;0]);//state evolution
+y=Pd.C*x;
+// simulate the observer
+x_hat=flts([u+0.01*rand(u);y+0.0001*rand(y)],O);
+clf;
+subplot(2,2,1)
+  plot2d(t',[x(1,:);x_hat(1,:)]'),
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_1=dy_1$', '$\hat{x_1}$');L.font_size=3;
+  xlabel('Time (s)')
+subplot(2,2,2)
+  plot2d(t',[x(2,:);x_hat(2,:)]')
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_2=dy_1^+$', '$\hat{x_2}$');L.font_size=3;
+  xlabel('Time (s)')
+subplot(2,2,3)
+  plot2d(t',[x(3,:);x_hat(3,:)]')
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_3=dy_2$', '$\hat{x_3}$');L.font_size=3;
+  xlabel('Time (s)')
+subplot(2,2,4)
+  plot2d(t',[x(4,:);x_hat(4,:)]')
+  e=gce();e.children.polyline_style=2;
+  L=legend('$x_4=dy_2^+$', '$\hat{x_4}$');L.font_size=3;
+  xlabel('Time (s)')]]>
+                </scilab:image>
+            </refsection>
+            <refsection>
+                <title>Reference</title>
+                <para>
+                    <ulink url="http://www.springer.com/us/book/9780817640095"> Engineering and Scientific Computing with Scilab</ulink>, Claude Gomez and al.,Springer Science+Business Media, LLC,1999, ISNB:978-1-4612-7204-5
+                </para>
+            </refsection>
+            <refsection role="see also">
+                <title>See also</title>
+                <simplelist type="inline">
+                    <member>
+                        <link linkend="lqr">lqr</link>
+                    </member>
+                    <member>
+                        <link linkend="observer">observer</link>
+                    </member>
+                    <member>
+                        <link linkend="obscont">obscont</link>
+                    </member>
+                    <member>
+                        <link linkend="lqg">lqg</link>
+                    </member>
+                    <member>
+                        <link linkend="fullrf">fullrf</link>
+                    </member>
+                </simplelist>
+            </refsection>
+        </refentry>
index b558977..e597481 100644 (file)
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>[K]=lqg(P,r)</synopsis>
+        <synopsis>K=lqg(P_aug,r)</synopsis>
+        <synopsis>K=lqg(P,Qxu,Qwv)</synopsis>
+        <synopsis>K=lqg(P,Qxu,Qwv,Qi,#dof)</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
         <variablelist>
             <varlistentry>
-                <term>P</term>
+                <term>P_aug</term>
                 <listitem>
                     <para>
-                        <literal>syslin</literal> list (augmented plant) in state-space form
+                        State space representation of the augmented plant (see:
+                        <link linkend="lqg2stan">lqg2stan</link>)
                     </para>
                 </listitem>
             </varlistentry>
                 <term>r</term>
                 <listitem>
                     <para>
-                        1x2 row vector = (number of measurements, number of inputs)  (dimension of  the 2,2 part of <literal>P</literal>)
+                        1 by 2 row vector = (number of measurements, number of
+                        inputs) (dimension of the 2,2 part of
+                        <literal>P_aug</literal>)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>P</term>
+                <listitem>
+                    <para>
+                        State-space representation of the nominal plant
+                        (<literal>nu</literal> inputs, <literal>ny</literal>
+                        outputs, <literal>nx</literal> states).
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
+                <term>Qxu</term>
+                <listitem>
+                    <para>
+                        Symmetric <literal>nx+nu</literal> by
+                        <literal>nx+nu</literal> weighting matrix.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Qwv</term>
+                <listitem>
+                    <para>
+                        Symmetric <literal>nx+ny</literal> by <literal>nx+ny</literal> covariance matrix.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Qi</term>
+                <listitem>
+                    <para>
+                        Symmetric <literal>ny</literal> by <literal>ny</literal> weight for integral term.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>#dof</term>
+                <listitem>
+                    <para>
+                        Scalar with value in {1,2}, the degrees of freedom of the
+                        controller. The default value is 2.
+                    </para>
+                </listitem>
+            </varlistentry>
+
+            <varlistentry>
                 <term>K</term>
                 <listitem>
                     <para>
-                        <literal>syslin</literal> list (controller)
+                        Linear LQG (H2) controller in state-space representation.
                     </para>
                 </listitem>
             </varlistentry>
     </refsection>
     <refsection>
         <title>Description</title>
+        <refsection>
+            <title>Regulation around zero</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata fileref="../../../images/lqg.png"/>
+                </imageobject>
+            </mediaobject>
+            <variablelist>
+                <varlistentry>
+                    <term>
+                        Syntax  <literal>K=lqg(P_aug,r)</literal>
+                    </term>
+                    <para>
+                        Computes the linear optimal LQG (H2) controller for the
+                        "augmented" plant <literal>P_aug</literal> which can be
+                        generated by <link linkend="lqg2stan">lqg2stan</link>
+                        givent the nominal plant plant <literal>P</literal>, the
+                        weighting matrix <literal>Qxu</literal> and the noise
+                        covariance matrix <literal>Qwv</literal>.
+                    </para>
+                </varlistentry>
+                <varlistentry>
+                    <term>
+                        Syntax  <literal>K=lqg(P,Qxu,Qwv)</literal>
+                    </term>
+                    <para>
+                        Computes the linear optimal LQG (H2) controller for the nominal
+                        plant <literal>P</literal>, the weighting matrix
+                        <literal>Qxu</literal> and the noise covariance matrix
+                        <literal>Qwv</literal>
+                    </para>
+                </varlistentry>
+            </variablelist>
+        </refsection>
+        <refsection>
+            <title>
+                Regulation around a reference signal, Syntax <literal>K=lqg(P,Qxu,Qwv,Qi [,#dof])</literal>
+            </title>
+            <para>
+                <mediaobject>
+                    <imageobject>
+                        <imagedata align="center" contentwidth="360" contentdepth="100"  fileref="../../../images/lqgi.png"/>
+                    </imageobject>
+                </mediaobject>
+            </para>
+            <para>
+                Computes the linear optimal LQG (H2) reference tracking controller for the
+                plant <literal>P</literal>, the weighting matrix
+                <literal>Qxu</literal> and the noise covariance matrix
+                <literal>Qwv</literal>
+            </para>
+        </refsection>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
         <para>
-            <literal>lqg</literal>  computes the linear optimal LQG (H2) controller for the
-            "augmented" plant <literal>P=syslin('c',A,B,C,D)</literal> (continuous time) or
-            <literal>P=syslin('d',A,B,C,D)</literal> (discrete time).
+            Assume the dynamical system formed by two masses connected by a spring and a damper:
         </para>
         <para>
-            The function <literal>lqg2stan</literal> returns <literal>P</literal> and <literal>r</literal> given the
-            nominal plant, weighting terms and variances of noises.
+            <mediaobject>
+                <imageobject>
+                    <imagedata fileref="../../../images/twoMasses.png"/>
+                </imageobject>
+            </mediaobject>
         </para>
         <para>
-            <literal>K</literal> is given by the following ABCD matrices:
-            <literal>[A+B*Kc+Kf*C+Kf*D*Kc,-Kf,Kc,0]</literal> where <literal>Kc=lqr(P12)</literal>
-            is the controller gain and <literal>Kf=lqe(P21)</literal> is the filter gain.
-            See example in <literal>lqg2stan</literal>.
+            A force <latex> u=\bar{u}+e</latex> (where <latex>e</latex> is a
+            noise) is applied to M, the deviations <latex>dy_1</latex> and
+            <latex>dy_2</latex> from equilibrium positions of the masses are
+            measured. These measures are subject to an additionnal
+            noise <latex>v</latex>.
         </para>
-    </refsection>
+        <para>
+            A continuous time state space representation of this system is:
+            <latex style="display"
+             align="left"><![CDATA[\left\lbrace\begin{array}{l}
+             \dot{x}=\left[\begin{array}{llll}0&1&0&0\\ -k/M&-b/M&k/M&b/M\\
+             0&0&0&1\\ k/m&b/m&-k/m&-b/m \end{array}\right] x
+             +\left[\begin{array}{l}0\\ 1/M\\ 0\\ 0 \end{array}\right]
+             (\bar{u}+e)\\ \left[\begin{array}{l}dy_1\\
+             dy_2\end{array}\right]=\left[\begin{array}{llll}1&0&0&0\\
+             0&0&1&0 \end{array}\right] x +v \end{array}\right.]]></latex>
+            <latex style="display" align="left">\text{Where }x=\left[\begin{array}{l}dy_1\\ \dot{dy_1}\\ dy_2\\
+                \dot{dy_2}\end{array}\right]
+            </latex>
+        </para>
+        <para>
+            The instructions below can be used to compute a LQG compensator
+            of the discretized version of this dynamical
+            system.  <latex valign="center">e</latex> and <latex>v</latex> are discrete
+            time white noises such as <latex style="display"
+      align="left">\mathbb{E}(e e')=Q_e \text{ , }\mathbb{E}(v
+                v')=R_vv \text{ and }\mathbb{E}(e v')=S_{ev}
+            </latex>
+        </para>
+        <para>
+            The LQ cost is defined by <latex style="display"
+      align="left"><![CDATA[\sum_0^\infty\left[\begin{array}{ll}x'&u'\end{array}\right]\left[\begin{array}{ll}Q_{xx}&0\\0&R_{uu}\end{array}\right]\left[\begin{array}{l}x\\u\end{array}\right]
+      dt]]></latex>
+        </para>
+        <refsection>
+            <title>Regulation around zero</title>
+            <programlisting role="example"><![CDATA[
+      // Form the state space model
+      M = 1; m = 0.2; k = 0.1; b = 0.004;
+      A = [0     1    0    0
+      -k/M  -b/M  k/M  b/M
+      0     0    0    1
+      k/m  b/m  -k/m  -b/m];
+      B = [0; 1/M; 0; 0];
+      C = [1 0 0 0  //dy1
+      0 0 1 0];//dy2
+      //inputs u and e; outputs dy1 and dy2
+      P = syslin("c",A, B, C);
+      // Discretize it
+      dt=0.5;
+      Pd=dscr(P, dt);
+
+      // The noise variances
+      Q_e=1; //additive input noise variance
+      R_vv=0.0001*eye(2,2); //measurement noise variance
+      Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
+      Qwv=sysdiag(Q_ww,R_vv);
+      //The compensator weights
+      Q_xx=diag([0.1 0 5 0]); //Weights on states
+      R_uu   = 0.3; //Weight on input
+      Qxu=sysdiag(Q_xx,R_uu);
+
+      //----syntax [K,X]=lqg(P,Qxu,Qwv)---
+      J=lqg(Pd,Qxu,Qwv);
+
+      //----syntax [K,X]=lqg(P_aug,r)---
+      // Form standard LQG model
+      [Paug,r]=lqg2stan(Pd,Qxu,Qwv); // Form standard LQG model
+      J1=lqg(Paug,r);
+
+      //  Form the closed loop
+      Sys=Pd/.(-J);
+      // Compare real and Estimated states for initial state evolution
+      t = 0:dt:30;
+      // Simulate system evolution for initial state [1;0;0;0;
+      y = flts(zeros(t),Sys,eye(8,1));
+      clf;
+      plot2d(t',y')
+      e=gce();e.children.polyline_style=2;
+      L=legend(["$dy_1$","$dy_2$"]);L.font_size=4;
+      xlabel('Time (s)')
+      ]]></programlisting>
+            <scilab:image>
+                // Form the state space model
+                M = 1; m = 0.2; k = 0.1; b = 0.004;
+                A = [0     1    0    0
+                -k/M  -b/M  k/M  b/M
+                0     0    0    1
+                k/m  b/m  -k/m  -b/m];
+                B = [0; 1/M; 0; 0];
+                C = [1 0 0 0  //dy1
+                0 0 1 0];//dy2
+                //inputs u and e; outputs dy1 and dy2
+                P = syslin("c",A, B, C);
+                // Discretize it
+                dt=0.5;
+                Pd=dscr(P, dt);
+
+                // The noise variances
+                Q_e=1; //additive input noise variance
+                R_vv=0.0001*eye(2,2); //measurement noise variance
+                Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
+                Qwv=sysdiag(Q_ww,R_vv);
+                //The compensator weights
+                Q_xx=diag([0.1 0 5 0]); //Weights on states
+                R_uu   = 0.3; //Weight on input
+                Qxu=sysdiag(Q_xx,R_uu);
+
+                //----syntax [K,X]=lqg(P,Qxu,Qwv)---
+                J=lqg(Pd,Qxu,Qwv);
+
+                //  Form the closed loop
+                Sys=Pd/.(-J);
+                // Compare real and Estimated states for initial state evolution
+                t = 0:dt:30;
+                // Simulate system evolution for initial state [1;0;0;0;
+                y = flts(zeros(t),Sys,eye(8,1));
+                clf;
+                plot2d(t',y')
+                e=gce();e.children.polyline_style=2;
+                L=legend(["$dy_1$","$dy_2$"]);L.font_size=4;
+                xlabel('Time (s)')
+            </scilab:image>
+        </refsection>
+        <refsection>
+            <title>
+                Regulation around a reference signal, Syntax <literal>K=lqg(P,Qxu,Qwv,Qi [,#dof])</literal>
+            </title>
+            <para>
+                The purpose of the controller is here to assign
+                <latex>dy_2</latex> using the measure of <latex>dy_2</latex>.
+            </para>
+            <programlisting role="example"><![CDATA[
+      M = 1; m = 0.2; k = 0.1; b = 0.004;
+      A = [0     1    0    0
+      -k/M  -b/M  k/M  b/M
+      0     0    0    1
+      k/m  b/m  -k/m  -b/m];
+      B = [0; 1/M; 0; 0];
+      C = [1 0 0 0  //dy1
+      0 0 1 0];//dy2
+      //inputs u and e; outputs dy1 and dy2
+      P = syslin("c",A, B, C);
+      // Discretize it
+      dt=0.1;
+      Pd=dscr(P, dt);
 
+      // The noise variances
+      Q_e=1; //additive input noise variance
+      R_vv=0.0001; //measurement noise variance
+      Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
+      Qwv=sysdiag(Q_ww,R_vv);
+      //The compensator weights
+      Q_xx=diag([0.1 0 1 0]); //Weights on states
+      R_uu   = 0.1; //Weight on input
+      Qxu=sysdiag(Q_xx,R_uu);
+
+      //Control of the second mass position (y2)
+      Qi=50;
+      J=lqg(Pd(2,:),Qxu,Qwv,Qi);
+      H=lft([1;1]*Pd(2,:)*(-J),1);
+      //step response
+      t=0:dt:15;
+      r=ones(t);
+      dy2=flts(r,H);
+      clf;
+      subplot(211);plot(t',dy2');xlabel("Time");ylabel("dy2")
+      u=flts([r;dy2],J);
+      subplot(212);plot(t',u');xlabel("Time");ylabel("u")
+      ]]>
+            </programlisting>
+            <scilab:image>
+                M = 1; m = 0.2; k = 0.1; b = 0.004;
+                A = [0     1    0    0
+                -k/M  -b/M  k/M  b/M
+                0     0    0    1
+                k/m  b/m  -k/m  -b/m];
+                B = [0; 1/M; 0; 0];
+                C = [1 0 0 0  //dy1
+                0 0 1 0];//dy2
+                //inputs u and e; outputs dy1 and dy2
+                P = syslin("c",A, B, C);
+                // Discretize it
+                dt=0.1;
+                Pd=dscr(P, dt);
+
+                // The noise variances
+                Q_e=1; //additive input noise variance
+                R_vv=0.0001; //measurement noise variance
+                Q_ww=Pd.B*Q_e*Pd.B'; //input noise adds to regular input u
+                Qwv=sysdiag(Q_ww,R_vv);
+                //The compensator weights
+                Q_xx=diag([0.1 0 1 0]); //Weights on states
+                R_uu   = 0.1; //Weight on input
+                Qxu=sysdiag(Q_xx,R_uu);
+
+                //Control of the second mass position (y2)
+                Qi=50;
+                J=lqg(Pd(2,:),Qxu,Qwv,Qi);
+                H=lft([1;1]*Pd(2,:)*J,1);
+                //step response
+                t=0:dt:15;
+                r=ones(t);
+                dy2=flts(r,H);
+                clf;
+                subplot(211);plot(t',dy2');xlabel("Time");ylabel("dy2")
+                u=flts([r;dy2],J);
+                subplot(212);plot(t',u');xlabel("Time");ylabel("u")
+            </scilab:image>
+        </refsection>
+    </refsection>
     <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-  s=poly(0,'s');
-  Plant=syslin('c',[1/(s+1)*s/(s-1)^2]);     //Nominal Plant
-  P22=tf2ss(Plant);    //...in state-space form
-  [ny,nu,nx]=size(P22);
-  rand('seed',0);rand('normal');
-  bigQ=rand(nx+nu,nx+nu);
-  bigQ=bigQ*bigQ';
-  bigR=rand(nx+ny,nx+ny);
-  bigR=bigR*bigR';  //random weighting matrices
-  [Plqg,r]=lqg2stan(P22,bigQ,bigR);     //LQG pb as a standard problem
-  Klqg=lqg(Plqg,r);          //Controller
-  spec(h_cl(Plqg,r,Klqg))    //Check internal stability
-  [Slqg,Rlqg,Tlqg]=sensi(P22,Klqg);  //Sensitivity functions
-  frq=logspace(-3,3);     //10^-3  to 10^3
-  y=svplot(Slqg);       //Computes singular values;
-  gainplot(frq,y)   //Plot sing. values
- ]]></programlisting>
-        <scilab:image>
-            s=poly(0,'s');
-            Plant=syslin('c',[1/(s+1)*s/(s-1)^2]);     //Nominal Plant
-            P22=tf2ss(Plant);    //...in state-space form
-            [ny,nu,nx]=size(P22);
-            rand('seed',0);rand('normal');
-            bigQ=rand(nx+nu,nx+nu);
-            bigQ=bigQ*bigQ';
-            bigR=rand(nx+ny,nx+ny);
-            bigR=bigR*bigR';  //random weighting matrices
-            [Plqg,r]=lqg2stan(P22,bigQ,bigR);     //LQG pb as a standard problem
-            Klqg=lqg(Plqg,r);          //Controller
-            spec(h_cl(Plqg,r,Klqg))    //Check internal stability
-            [Slqg,Rlqg,Tlqg]=sensi(P22,Klqg);  //Sensitivity functions
-            frq=logspace(-3,3);     //10^-3  to 10^3
-            y=svplot(Slqg);       //Computes singular values;
-            gainplot(frq,y)   //Plot sing. values
-        </scilab:image>
+        <title>Reference</title>
+        <para>
+            <ulink url="http://www.springer.com/us/book/9780817640095"> Engineering and Scientific Computing with Scilab</ulink>, Claude Gomez and al.,Springer Science+Business Media, LLC,1999, ISNB:978-1-4612-7204-5
+        </para>
     </refsection>
     <refsection role="see also">
-        <title>See also</title>
+        <title>See Also</title>
         <simplelist type="inline">
             <member>
                 <link linkend="lqg2stan">lqg2stan</link>
diff --git a/scilab/modules/cacsd/help/en_US/control_design/linear_quadratic/lqi.xml b/scilab/modules/cacsd/help/en_US/control_design/linear_quadratic/lqi.xml
new file mode 100644 (file)
index 0000000..d8694e4
--- /dev/null
@@ -0,0 +1,185 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) INRIA -
+ *
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="lqi">
+    <refnamediv>
+        <refname>lqi</refname>
+        <refpurpose>Linear quadratic integral compensator (full state)  </refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Syntax</title>
+        <synopsis>[K,X]=lqi(P,Q,R [,S])</synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
+            <varlistentry>
+                <term>P</term>
+                <listitem>
+                    <para>
+                        The plant  state space representation
+                        (see <link linkend="syslin">syslin</link>) with nx states, nu inputs and ny outputs.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Q</term>
+                <listitem>
+                    <para>
+                        Real nx+ny by nx+ny symmetric matrix,
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>R</term>
+                <listitem>
+                    <para>
+                        full rank nu by nu real symmetric matrix
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>S</term>
+                <listitem>
+                    <para>
+                        real nx+ny by nu  matrix, the default value is zeros(nx+ny,nu)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>K</term>
+                <listitem>
+                    <para>a real matrix, the optimal gain</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>a real symmetric matrix, the stabilizing solution of the Riccati equation</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            This function computes the linear quadratic integral
+            full-state gain K for the plant P. The associated system
+            block diagram is:
+        </para>
+        <para>
+            <inlinemediaobject>
+                <imageobject>
+                    <imagedata fileref="../../../images/lqi.png"/>
+                </imageobject>
+            </inlinemediaobject>
+        </para>
+        <para>
+            The plant P is given by its state space representation
+            <latex style="display">\text{P}=\left\lbrace \begin{array}{l}\dot{x}=A x+B u\\y=C x+D u \end{array}\right. \text{ in continuous time or } \text{P}=\left\lbrace \begin{array}{l}\overset{+}{x}=A x+B_2 u\\y=C x+D u \end{array}\right. \text{ in discrete time.}</latex>
+            The cost function in l2-norm is:
+            <latex style="display">\int_{t=0}^\infty{z(t)' Q z(t)+u(t)' R u(t)+2 z(t) S u(t) dt}\text{ in continuous time } </latex>
+            <latex style="display">\sum_{k=0}^\infty{z(k)' Q z(k)+u(k)' R u(k)+2 z(k) S u(k)}\text{ in discrete time.}</latex>
+            where <latex>z=\left[\begin{array}{l}x\\x_i \end{array}\right]</latex> and <latex>x_i</latex> is the integrator(s) state(s);
+        </para>
+    </refsection>
+    <refsection>
+        <title>Algorithm</title>
+        <para>
+            The lqi function solves the <link linkend="lqr">lqr</link> problem for the augmented plant
+            <latex style="display"><![CDATA[\left\lbrace \begin{array}{l}\left[\begin{array}{l}\dot{x}\\ \dot{x_i} \end{array}\right]=\left[\begin{array}{ll}A&0\\-C&0 \end{array}\right]\left[\begin{array}{l}x\\x_i \end{array}\right]+\left[\begin{array}{l}B\\-G \end{array}\right] u \end{array}\right. \text{ in continuous time }]]></latex>
+            <latex style="display"><![CDATA[\text{P}=\left\lbrace\begin{array}{l}\left[\begin{array}{l}\overset{+}{x}\\ \overset{+}{x_i} \end{array}\right]=\left[\begin{array}{ll}A&0\\-C dt&I \end{array}\right]\left[\begin{array}{l}x\\x_i \end{array}\right]+\left[\begin{array}{l}B\\-G dt \end{array}\right] u \end{array} \right.\text{ in discrete time }]]>
+            </latex>
+        </para>
+    </refsection>
+    <refsection>
+        <title>Caution</title>
+        <para>
+            It is assumed that matrix <latex>R</latex> is non singular.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Remark</title>
+        <para>
+            If the full state of the system is not available, An estimator
+            of the plant state can be built using the <link
+      linkend="lqe">lqe</link> function.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <para>
+            Linear quadratic integral controller of a simplified disk drive using state observer.
+        </para>
+        <para>
+            <inlinemediaobject>
+                <imageobject>
+                    <imagedata fileref="../../../images/lqifull.png"/>
+                </imageobject>
+            </inlinemediaobject>
+        </para>
+        <programlisting role="example"><![CDATA[
+    //Disk drive model
+    G=syslin("c",[0,32;-31.25,-0.4],[0;2.236068],[0.0698771,0]);
+    t=linspace(0,20,2000);
+    y=csim("step",t,G);
+
+    //State estimator
+    Wy=1;
+    Wu=1;
+    S=0;
+    Q=G.B*Wu*G.B';
+    R=Wy+G.D*S + S'*G.D+G.D*Wu*G.D';
+    S=G.B*Wu*G.D'+S;
+
+    //State estimator
+    [Kf,X]=lqe(G,Q,R,S);
+    Gx=observer(G,Kf);
+
+    //LQI compensator
+
+    wy=100;
+    Q= wy*sysdiag(G.C'*G.C,1);
+    R=1/wy;
+    Kc=lqi(G,Q,R);
+    //full controller
+    K=lft([1;1]*(-Kc(1:2)*Gx(:,[2 1])+Kc(3)*[1/%s 0]),1);//e-->u
+
+    //Full system
+    H=(-K*G)/.(1);// full system transfer function
+
+    y=csim("step",t,H);
+    clf;plot(t,y)
+    ]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="observer">observer</link>
+            </member>
+
+            <member>
+                <link linkend="lqr">lqr</link>
+            </member>
+            <member>
+                <link linkend="lqg">lqg</link>
+            </member>
+            <member>
+                <link linkend="lft">lft</link>
+            </member>
+        </simplelist>
+    </refsection>
+</refentry>
index 765d173..d937dbb 100644 (file)
@@ -21,6 +21,7 @@
     <refsynopsisdiv>
         <title>Syntax</title>
         <synopsis>[K,X]=lqr(P12)</synopsis>
+        <synopsis>[K,X]=lqr(P,Q,R [,S])</synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
                 <term>P12</term>
                 <listitem>
                     <para>
-                        <literal>syslin</literal> list (state-space linear system)
+                        A state space representation of a linear
+                        dynamical system (see <link
+            linkend="syslin">syslin</link>)
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>K,X</term>
+                <term>P</term>
                 <listitem>
-                    <para>two real matrices</para>
+                    <para> A state space representation of a linear
+                        dynamical system (see <link
+          linkend="syslin">syslin</link>)
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>Q</term>
+                <listitem>
+                    <para>
+                        Real symmetric matrix, with same dimensions as P.A
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>R</term>
+                <listitem>
+                    <para>
+                        full rank real symmetric matrix
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>S</term>
+                <listitem>
+                    <para>
+                        real matrix, the default value is <code>zeros(size(R,1),size(Q,2))</code>
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>K</term>
+                <listitem>
+                    <para>a real matrix, the optimal gain</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X</term>
+                <listitem>
+                    <para>a real symmetric matrix, the stabilizing
+                        solution of the Riccati equation
+                    </para>
                 </listitem>
             </varlistentry>
         </variablelist>
     </refsection>
     <refsection>
         <title>Description</title>
+        <variablelist>
+            <varlistentry>
+                <term>
+                    Syntax  <literal>[K,X]=lqr(P)</literal>
+                </term>
+                <listitem>
+                    <para>
+                        Computes the linear optimal LQ full-state gain K  for the state space representation P
+                        <latex style="display">\left\{\begin{array}{l}\dot{x}=A x+B u\\z=C x+D u\end{array}\right. \text{ in continuous time or }
+                            \left\{\begin{array}{l}x^+=A x+B u\\z=C x+D u\end{array}\right.
+                            \text{ in discrete time.}
+                        </latex>
+
+                        And instantaneous cost function in l2-norm:
+                        <latex style="display"><![CDATA[\left[\begin{array}{ll}x'&u'\end{array}\right]  BigQ  \left[\begin{array}{l}x\\u\end{array}\right] \text{ where }BigQ=\left[\begin{array}{l}C'\\D'\end{array}\right] \left[\begin{array}{ll}C&D\end{array}\right]=\left[\begin{array}{ll}Q&S'\\S&R\end{array}\right]]]></latex>
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry><term>Syntax <literal>[K,X]=lqr(P,Q,R [,S])</literal></term><listitem>
+      <para>
+        Computes the linear optimal LQ full-state gain K for the linear dynamical system P:
+        <latex style="display">\dot{x}=A x+B u \text{ in continuous time or }x^+=A x+B u \text{ in discrete time.}</latex>
+        And  instantaneous cost function in l2-norm:
+        <latex style="display"><![CDATA[\left[\begin{array}{ll}x'&u'\end{array}\right]  BigQ  \left[\begin{array}{l}x\\u\end{array}\right]\text{ where }BigQ=\left[\begin{array}{ll}Q&S'\\S&R\end{array}\right]]]></latex>
+      </para>
+      <note>
+        <title>Remark</title>
         <para>
-            <literal>lqr</literal>  computes the linear optimal LQ full-state gain
-            for the plant <literal>P12=[A,B2,C1,D12]</literal> in continuous or
-            discrete time.
-        </para>
-        <para>
-            <literal>P12</literal> is a <literal>syslin</literal> list (e.g. <literal>P12=syslin('c',A,B2,C1,D12)</literal>).
-        </para>
-        <para>
-            The cost function is l2-norm of <literal>z'*z</literal> with <literal>z=C1 x + D12 u</literal>
-            i.e. <literal>[x,u]' * BigQ * [x;u]</literal> where
-        </para>
-        <programlisting role=""><![CDATA[
-      [C1' ]               [Q  S]
-BigQ= [    ]  * [C1 D12] = [    ]
-      [D12']               [S' R]
- ]]></programlisting>
-        <para>
-            The gain <literal>K</literal> is such that <literal>A + B2*K</literal> is stable.
-        </para>
-        <para>
-            <literal>X</literal> is the stabilizing solution of the Riccati equation.
-        </para>
-        <para>
-            For a continuous plant:
-        </para>
-        <programlisting role=""><![CDATA[
-(A-B2*inv(R)*S')'*X+X*(A-B2*inv(R)*S')-X*B2*inv(R)*B2'*X+Q-S*inv(R)*S'=0
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-inv(R)*(B2'*X+S)
- ]]></programlisting>
-        <para>
-            For a discrete plant:
-        </para>
-        <programlisting role=""><![CDATA[
-X=A'*X*A-(A'*X*B2+C1'*D12)*pinv(B2'*X*B2+D12'*D12)*(B2'*X*A+D12'*C1)+C1'*C1;
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-pinv(B2'*X*B2+D12'*D12)*(B2'*X*A+D12'*C1)
- ]]></programlisting>
-        <para>
-            An equivalent form for <literal>X</literal> is
-        </para>
-        <programlisting role=""><![CDATA[
-X=Abar'*inv(inv(X)+B2*inv(r)*B2')*Abar+Qbar
- ]]></programlisting>
-        <para>
-            with <literal>Abar=A-B2*inv(R)*S'</literal> and <literal>Qbar=Q-S*inv(R)*S'</literal>
-        </para>
-        <para>
-            The 3-blocks matrix pencils associated with these Riccati equations are:
-        </para>
-        <programlisting role=""><![CDATA[
-             discrete                           continuous
- |I   0    0|   | A    0    B2|         |I   0   0|   | A    0    B2|
-z|0   A'   0| - |-Q    I    -S|        s|0   I   0| - |-Q   -A'   -S|
- |0   B2'  0|   | S'   0     R|         |0   0   0|   | S'  -B2'   R|
- ]]></programlisting>
-        <para>
-            <warning>
-                Caution: It is assumed that matrix R is non singular. In particular,
-                the plant must be tall (number of outputs &gt;= number of inputs).
-            </warning>
+          In this case the P.C and P.D componants of the system  are ignored
         </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-A=rand(2,2);B=rand(2,1);   //two states, one input
-Q=diag([2,5]);R=2;     //Usual notations x'Qx + u'Ru
-Big=sysdiag(Q,R);    //Now we calculate C1 and D12
-[w,wp]=fullrf(Big);C1=wp(:,1:2);D12=wp(:,3:$);   //[C1,D12]'*[C1,D12]=Big
-P=syslin('c',A,B,C1,D12);    //The plant (continuous-time)
-[K,X]=lqr(P)
-spec(A+B*K)    //check stability
-norm(A'*X+X*A-X*B*inv(R)*B'*X+Q,1)  //Riccati check
-P=syslin('d',A,B,C1,D12);    // Discrete time plant
-[K,X]=lqr(P)
-spec(A+B*K)   //check stability
-norm(A'*X*A-(A'*X*B)*pinv(B'*X*B+R)*(B'*X*A)+Q-X,1) //Riccati check
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqe">lqe</link>
-            </member>
-            <member>
-                <link linkend="gcare">gcare</link>
-            </member>
-            <member>
-                <link linkend="leqr">leqr</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
+      </note>
+    </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Algorithm</title>
+    <itemizedlist>
+      <listitem><para>
+        For a continuous plant, if <latex>\text{X}</latex> is the stabilizing solution of the Riccati equation:
+        <latex style="display" align="center">(A-B R^{-1}S)'\text{X}+\text{X} (A-B R^{-1} S)-\text{X} B R^{-1} B' \text{X}+Q-S' R^{-1} S=0</latex>
+        the linear optimal LQ full-state gain K is given by <latex  style="display" align="center">\text{K}=-R^{-1} (B' \text{X}+S')</latex>
+      </para></listitem>
+      <listitem><para>
+        For a discrete plant, if <latex>\text{X}</latex> is the stabilizing solution of the Riccati equation:
+        <latex style="display"  align="center">A' \text{X} A-\text{X}-(A' \text{X} B+S') (B' \text{X} B+R)^{+} (B' \text{X} A+S)+Q=0</latex>
+        the linear optimal LQ full-state gain K is given by <latex  style="display" align="center" > \text{K}=-(B' \text{X} B+R)^{+} (B' \text{X} A+S)</latex>
+      </para>
+      <para>
+        An equivalent form for the equation is
+        <latex style="display"  align="center">(\overline{A}' \text{X}^{-1}+B R^{-1} B') \overline{A}+\overline{Q}-\text{X}=0</latex>
+        with <latex style="display" align="center">\overline{A}=A-B R^{-1} S'\text{ and }\overline{Q}=Q-S R^{-1} S'</latex>
+      </para></listitem>
+    </itemizedlist>
+    <para>
+      The gain <literal>K</literal> is such that <latex>A + B \text{K}</latex> is stable.
+    </para>
+    <para>
+      The resolution of the Riccati equation is obtained by  <link linkend="schur">schur</link> factorization of the 3-blocks matrix pencils associated with these Riccati equations:
+      <itemizedlist>
+        <listitem><para>For a continuous plant
+        <latex style="display"> <![CDATA[s\left[\begin{array}{lll}I&0&0\\0&I&0\\0&0&0\end{array}\right]-\left[\begin{array}{lll}A&0&B\\-Q&-A'&-S'\\S&-B'&R\end{array}\right]]]></latex>
+        </para></listitem>
+        <listitem><para>For a discrete time plant
+        <latex style="display"><![CDATA[z\left[\begin{array}{lll}I&0&0\\0&A'&0\\0&-B'&0\end{array}\right]-\left[\begin{array}{lll}A&0& B\\-Q&I&-S'\\S&0& R\end{array}\right]]]></latex>
+        </para></listitem>
+      </itemizedlist>
+    </para>
+  </refsection>
+  <refsection>
+    <title>Caution</title>
+    <para>
+      It is assumed that matrix <latex>R</latex> or <latex>D' D</latex> is non singular.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Remark</title>
+    <para>
+      If the full state of the system is not available, An estimator can be built using the <link linkend="lqe">lqe</link> or the <link linkend="lqg">lqg</link> function.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Examples</title>
+    <para>
+      Assume the dynamical system formed by two masses connected by a spring and a damper:
+      <mediaobject>
+        <imageobject>
+          <imagedata fileref="../../../images/twoMasses.png"/>
+        </imageobject>
+      </mediaobject>
+      A force <latex> u=\bar{u}+e</latex> (where <latex>e</latex>
+      is a noise) is applied to the big one. Here it is assumed
+      that the deviations from equilibrium positions of the mass
+      <latex>dy_1</latex> and <latex>dy_2</latex> positions has
+      well as their derivatives are measured.
+    </para>
+    <para>
+      A state space representation of this system is:
+      <latex style="display" align="left"><![CDATA[
+      \dot{x}=\left[\begin{array}{llll}0&1&0&0\\
+      -k/M&-b/M&k/M&b/M\\ 0&0&0&1\\ k/m&b/m&-k/m&-b/m
+      \end{array}\right] x +\left[\begin{array}{l}0\\ 1/M\\ 0\\ 0
+      \end{array}\right] u]]></latex>
+                        <latex style="display" align="left">\text{Where }x=\left[\begin{array}{l}dy_1\\ \dot{dy_1}\\ dy_2\\
+                            \dot{dy_2}\end{array}\right]
+                        </latex>
+                    </para>
+                    <para>
+                        The LQ cost is defined by <latex style="display"
+      align="left"><![CDATA[\int_0^\infty\left[\begin{array}{ll}x'&u'\end{array}\right]\left[\begin{array}{ll}Q_{xx}&0\\0&R_{uu}\end{array}\right]\left[\begin{array}{l}x\\u\end{array}\right]
+      dt]]></latex>
+                    </para>
+                    <para>The following instructions may be used to compute a LQ compensator of this dynamical system.</para>
+                    <programlisting role="example"><![CDATA[
+    // Form the state space model (assume full state output)
+    M = 1; m = 0.2; k = 0.1; b = 0.004;
+    A = [  0     1    0    0
+    -k/M  -b/M  k/M  b/M
+    0     0    0    1
+    k/m  b/m  -k/m  -b/m];
+    B = [0; 1/M; 0; 0];
+    C = eye(4,4);
+    P = syslin("c",A, B, C);
+    //The compensator weights
+    Q_xx=diag([15 0 3 0]); //Weights on states
+    R_uu   = 0.5; //Weight on input
+    Kc=lqr(P,Q_xx,R_uu);
+
+    //form the Plant+compensator system
+
+    C=[1 0 0 0  //dy1
+    0 0 1 0];//dy2
+    S=C*(P/.(-Kc));
+    //check system stability
+    and(real(spec(S.A))<0)
+    // Check by simulation
+    dt=0.1;
+    t=0:dt:30;
+    u=0.1*rand(t);
+    y=csim(u,t,S,[1;0;0;0]);
+    clf;plot(t',y');xlabel(_("time (s)"))
+    L=legend(["$dy_1$","$dy_2$"]);L.font_size=4;
+    ]]></programlisting>
+
+                    <scilab:image><![CDATA[
+    // Form the state space model (assume full state output)
+    M = 1; m = 0.2; k = 0.1; b = 0.004;
+    A = [  0     1    0    0
+    -k/M  -b/M  k/M  b/M
+    0     0    0    1
+    k/m  b/m  -k/m  -b/m];
+    B = [0; 1/M; 0; 0];
+    C = eye(4,4);
+    P = syslin("c",A, B, C);
+    //The compensator weights
+    Q_xx=diag([15 0 3 0]); //Weights on states
+    R_uu   = 0.5; //Weight on input
+    Kc=lqr(P,Q_xx,R_uu);
+
+    //form the Plant+compensator system
+
+    C=[1 0 0 0  //dy1
+    0 0 1 0];//dy2
+    S=C*(P/.(-Kc));
+    //check system stability
+    and(real(spec(S.A))<0)
+    // Check by simulation
+    dt=0.1;
+    t=0:dt:30;
+    u=0.1*rand(t);
+    y=csim(u,t,S,[1;0;0;0]);
+    clf;plot(t',y');xlabel(_("time (s)"))
+    L=legend(["$dy_1$","$dy_2$"]);L.font_size=4;
+    ]]>
+                    </scilab:image>
+                </refsection>
+                <refsection>
+                    <title>Reference</title>
+                    <para>
+                        <ulink url="http://www.springer.com/us/book/9780817640095"> Engineering and Scientific Computing with Scilab</ulink>, Claude Gomez and al.,Springer Science+Business Media, LLC,1999, ISNB:978-1-4612-7204-5
+                    </para>
+                </refsection>
+                <refsection role="see also">
+                    <title>See also</title>
+                    <simplelist type="inline">
+                        <member>
+                            <link linkend="lqg">lqg</link>
+                        </member>
+                        <member>
+                            <link linkend="lqe">lqe</link>
+                        </member>
+                        <member>
+                            <link linkend="gcare">gcare</link>
+                        </member>
+                        <member>
+                            <link linkend="leqr">leqr</link>
+                        </member>
+                        <member>
+                            <link linkend="riccati">riccati</link>
+                        </member>
+                        <member>
+                            <link linkend="schur">schur</link>
+                        </member>
+                    </simplelist>
+                </refsection>
+            </refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/control_loop/augment.xml b/scilab/modules/cacsd/help/fr_FR/control_design/control_loop/augment.xml
deleted file mode 100644 (file)
index 1067129..0000000
+++ /dev/null
@@ -1,161 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="augment">
-    <refnamediv>
-        <refname>augment</refname>
-        <refpurpose>augmented plant</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[P,r]=augment(G)
-            [P,r]=augment(G,flag1)
-            [P,r]=augment(G,flag1,flag2)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>G</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the nominal plant
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag1</term>
-                <listitem>
-                    <para>
-                        one of the following (upper case) character string: <literal> 'S' </literal>, <literal> 'R' </literal>, <literal> 'T' </literal> <literal> 'SR' </literal>, <literal> 'ST' </literal>, <literal> 'RT' </literal> <literal> 'SRT' </literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag2</term>
-                <listitem>
-                    <para>
-                        one of the following character string: <literal> 'o' </literal> (stands for 'output', this is the default value) or <literal>'i'</literal> (stands for 'input').
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the ``augmented'' plant
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 row vector, dimension of <literal>P22 = G</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            If <literal>flag1='SRT'</literal> (default value), returns the "full" augmented plant
-        </para>
-        <programlisting role=""><![CDATA[
-    [ I | -G]   -->'S'
-    [ 0 |  I]   -->'R'
-P = [ 0 |  G]   -->'T'
-    [-------]
-    [ I | -G]
- ]]></programlisting>
-        <para>
-            <literal> 'S' </literal>, <literal> 'R' </literal>, <literal> 'T' </literal> refer to the first three (block) rows
-            of <literal>P</literal> respectively.
-        </para>
-        <para>
-            If one of these letters is absent in <literal>flag1</literal>, the corresponding
-            row in <literal>P</literal> is missing.
-        </para>
-        <para>
-            If <literal>G</literal> is given in state-space form, the returned <literal>P</literal> is minimal.
-            <literal>P</literal> is calculated by: <literal>[I,0,0;0,I,0;-I,0,I;I,0,0]*[I,-G;0,I;I,0]</literal>.
-        </para>
-        <para>
-            The augmented plant associated with input sensitivity functions, namely
-        </para>
-        <programlisting role=""><![CDATA[
-    [ I | -I]   -->'S'  (input sensitivity)
-    [ G | -G]   -->'R'  (G*input sensitivity)
-P = [ 0 |  I]   -->'T'  (K*G*input sensitivity)
-    [-------]
-    [ G | -G]
-    ]]></programlisting>
-        <para>
-            is obtained by the command <literal>[P,r]=augment(G,flag,'i')</literal>. For
-            state-space <literal>G</literal>, this <literal>P</literal>
-            is calculated by: <literal>[I,-I;0,0;0,I;0,0]+[0;I;0;I]*G*[I,-I]</literal>
-            and is thus generically minimal.
-        </para>
-        <para>
-            Note that weighting functions can be introduced by left-multiplying
-            <literal>P</literal> by a diagonal system of appropriate dimension, e.g.,
-            <literal> P = sysdiag(W1,W2,W3,eye(G))*P</literal>.
-        </para>
-        <para>
-            Sensitivity functions can be calculated by <literal>lft</literal>. One has:
-        </para>
-        <para>
-            For output sensitivity functions [P,r]=augment(P,'SRT'):
-            lft(P,r,K)=[inv(eye()+G*K);K*inv(eye()+G*K);G*K*inv(eye()+G*K)];
-        </para>
-        <para>
-            For input sensitivity functions [P,r]=augment(P,'SRT','i'):
-            lft(P,r,K)=[inv(eye()+K*G);G*inv(eye()+K*G);K*G*inv(eye()+G*K)];
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-G=ssrand(2,3,2); //Plant
-K=ssrand(3,2,2); //Compensator
-[P,r]=augment(G,'T');
-T=lft(P,r,K);   //Complementary sensitivity function
-Ktf=ss2tf(K);Gtf=ss2tf(G);
-Ttf=ss2tf(T);T11=Ttf(1,1);
-Oloop=Gtf*Ktf;
-Tn=Oloop*inv(eye(Oloop)+Oloop);
-clean(T11-Tn(1,1));
-//
-[Pi,r]=augment(G,'T','i');
-T1=lft(Pi,r,K);T1tf=ss2tf(T1); //Input Complementary sensitivity function
-Oloop=Ktf*Gtf;
-T1n=Oloop*inv(eye(Oloop)+Oloop);
-clean(T1tf(1,1)-T1n(1,1))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lft">lft</link>
-            </member>
-            <member>
-                <link linkend="sensi">sensi</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/control_loop/feedback.xml b/scilab/modules/cacsd/help/fr_FR/control_design/control_loop/feedback.xml
deleted file mode 100644 (file)
index fa23b74..0000000
+++ /dev/null
@@ -1,97 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="feedback">
-    <refnamediv>
-        <refname>feedback</refname>
-        <refpurpose>feedback operation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>Sl=Sl1/.Sl2</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sl1,Sl2</term>
-                <listitem>
-                    <para>
-                        linear systems (<literal>syslin</literal> list) in state-space or transfer form, or ordinary gain matrices.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Sl</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list) in state-space or transfer form
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            The feedback operation is denoted by <literal> /. </literal> (slashdot).
-            This command returns <literal>Sl=Sl1*(I+Sl2*Sl1)^-1</literal>, i.e the (negative)
-            feedback of <literal>Sl1</literal> and <literal>Sl2</literal>. <literal>Sl</literal> is the transfer
-            <literal> v -&gt; y</literal> for <literal> y = Sl1 u</literal>, <literal>u = v - Sl2 y</literal>.
-        </para>
-        <para>
-            The result is the same as <literal>Sl=LFT([0,I;I,-Sl2],Sl1)</literal>.
-        </para>
-        <para>
-            <warning>
-                Caution: do not use with decimal point (e.g. <literal>1/.1</literal> is ambiguous!)
-            </warning>
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-S1=ssrand(2,2,3);S2=ssrand(2,2,2);
-W=S1/.S2;
-ss2tf(S1/.S2)
-//Same operation by LFT:
-ss2tf(lft([zeros(2,2),eye(2,2);eye(2,2),-S2],S1))
-//Other approach: with constant feedback
-BigS=sysdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
-Bigclosed=BigS/.F;
-W1=Bigclosed(1:2,1:2);   //W1=W (in state-space).
-ss2tf(W1)
-//Inverting
-ss2tf(S1*inv(eye()+S2*S1))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lft">lft</link>
-            </member>
-            <member>
-                <link linkend="sysdiag">sysdiag</link>
-            </member>
-            <member>
-                <link linkend="augment">augment</link>
-            </member>
-            <member>
-                <link linkend="obscont">obscont</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/control_loop/lft.xml b/scilab/modules/cacsd/help/fr_FR/control_design/control_loop/lft.xml
deleted file mode 100644 (file)
index 07fb54e..0000000
+++ /dev/null
@@ -1,144 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lft">
-    <refnamediv>
-        <refname>lft</refname>
-        <refpurpose>linear fractional transformation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[P1]=lft(P,K)
-            [P1]=lft(P,r,K)
-            [P1,r1]=lft(P,r,Ps,rs)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the ``augmented'' plant, implicitly partitioned into four blocks (two input ports and two output ports).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the controller (possibly an ordinary gain).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 row vector, dimension of <literal>P22</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Ps  </term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), implicitly partitioned into four blocks (two input ports and two output ports).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rs  </term>
-                <listitem>
-                    <para>
-                        1x2 row vector, dimension of <literal>Ps22</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Linear fractional transform between two standard plants
-            <literal>P</literal> and <literal>Ps</literal> in state space form or in
-            transfer form (<literal>syslin</literal> lists).
-        </para>
-        <para>
-            <literal>r= size(P22) rs=size(P22s)</literal>
-        </para>
-        <para>
-            <literal>lft(P,r, K)</literal> is the linear fractional transform
-            between <literal>P</literal> and a controller <literal>K</literal>
-            (<literal>K</literal> may be a gain or a controller in state space form
-            or in transfer form);
-        </para>
-        <para>
-            <literal>lft(P,K)</literal> is <literal>lft(P,r,K)</literal> with
-            <literal>r</literal>=size of <literal>K</literal> transpose;
-        </para>
-        <para>
-            <literal>P1= P11+P12*K* (I-P22*K)^-1 *P21</literal>
-        </para>
-        <para>
-            <literal>[P1,r1]=lft(P,r,Ps,rs)</literal> returns the generalized (2
-            ports) lft of <literal>P</literal> and <literal>Ps</literal>.
-        </para>
-        <para>
-            <literal>P1</literal> is the pair two-port interconnected plant and the
-            partition of <literal>P1</literal> into 4 blocks in given by
-            <literal>r1</literal> which is the dimension of the <literal>22</literal>
-            block of <literal>P1</literal>.
-        </para>
-        <para>
-            <literal>P</literal> and <literal>R</literal> can be PSSDs i.e. may admit a
-            polynomial <literal>D</literal> matrix.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-s=poly(0,'s');
-P=[1/s, 1/(s+1); 1/(s+2),2/s]; K= 1/(s-1);
-lft(P,K)
-lft(P,[1,1],K)
-P(1,1)+P(1,2)*K*inv(1-P(2,2)*K)*P(2,1)   //Numerically dangerous!
-ss2tf(lft(tf2ss(P),tf2ss(K)))
-lft(P,-1)
-f=[0,0;0,1];w=P/.f; w(1,1)
-//Improper plant (PID control)
-W=[1,1;1,1/(s^2+0.1*s)];K=1+1/s+s
-lft(W,[1,1],K); ss2tf(lft(tf2ss(W),[1,1],tf2ss(K)))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="sensi">sensi</link>
-            </member>
-            <member>
-                <link linkend="augment">augment</link>
-            </member>
-            <member>
-                <link linkend="feedback">feedback</link>
-            </member>
-            <member>
-                <link linkend="sysdiag">sysdiag</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/disturbance_decoupling/ddp.xml b/scilab/modules/cacsd/help/fr_FR/control_design/disturbance_decoupling/ddp.xml
deleted file mode 100644 (file)
index 0c90aa5..0000000
+++ /dev/null
@@ -1,175 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="ddp">
-    <refnamediv>
-        <refname>ddp</refname>
-        <refpurpose>disturbance decoupling</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[Closed,F,G]=ddp(Sys,zeroed,B1,D1)
-            [Closed,F,G]=ddp(Sys,zeroed,B1,D1,flag,alfa,beta)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sys</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list containing the matrices <literal>(A,B2,C,D2)</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>zeroed</term>
-                <listitem>
-                    <para>
-                        integer vector, indices of outputs of <literal>Sys</literal> which are zeroed.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>B1</term>
-                <listitem>
-                    <para>real matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>D1</term>
-                <listitem>
-                    <para>
-                        real matrix. <literal>B1</literal> and <literal>D1</literal> have the same number of columns.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag</term>
-                <listitem>
-                    <para>
-                        string <literal>'ge'</literal> or <literal>'st'</literal> (default) or <literal>'pp'</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>alpha</term>
-                <listitem>
-                    <para>real or complex vector (loc. of closed loop poles)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>beta</term>
-                <listitem>
-                    <para>real or complex vector (loc. of closed loop poles)</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Exact disturbance decoupling (output nulling algorithm).
-            Given a linear system, and a subset of outputs, z, which are to
-            be zeroed, characterize the inputs w of Sys such that the
-            transfer function from w to z is zero.
-            <literal>Sys</literal> is a linear system {A,B2,C,D2} with one input and two outputs
-            ( i.e.  Sys: u--&gt;(z,y) ), part the following system defined from <literal>Sys</literal>
-            and <literal>B1,D1</literal>:
-        </para>
-        <programlisting role=""><![CDATA[
-xdot =  A x + B1  w + B2  u
-   z = C1 x + D11 w + D12 u
-   y = C2 x + D21 w + D22 u
- ]]></programlisting>
-        <para>
-            outputs of Sys are partitioned into (z,y) where z is to be zeroed,
-            i.e. the matrices C and D2 are:
-        </para>
-        <programlisting role=""><![CDATA[
-C=[C1;C2]         D2=[D12;D22]
-C1=C(zeroed,:)    D12=D2(zeroed,:)
- ]]></programlisting>
-        <para>
-            The matrix <literal>D1</literal> is partitioned similarly as <literal>D1=[D11;D21]</literal>
-            with <literal>D11=D1(zeroed,:)</literal>.
-            The control is u=Fx+Gw and one  looks for matriced <literal>F,G</literal> such that the
-            closed loop system: w--&gt;z given by
-        </para>
-        <programlisting role=""><![CDATA[
-xdot= (A+B2*F)  x + (B1 + B2*G) w
-  z = (C1+D12F) x + (D11+D12*G) w
- ]]></programlisting>
-        <para>
-            has zero transfer transfer function.
-        </para>
-        <para>
-            <literal>flag='ge'</literal>no stability constraints.
-            <literal>flag='st'</literal> : look for stable closed loop system (A+B2*F stable).
-            <literal>flag='pp'</literal> : eigenvalues of A+B2*F are assigned to <literal>alfa</literal> and
-            <literal>beta</literal>.
-        </para>
-        <para>
-            Closed is a realization of the <literal>w--&gt;y</literal> closed loop system
-        </para>
-        <programlisting role=""><![CDATA[
-xdot= (A+B2*F)  x + (B1 + B2*G) w
-  y = (C2+D22*F) x + (D21+D22*G) w
- ]]></programlisting>
-        <para>
-            Stability (resp. pole placement) requires stabilizability
-            (resp. controllability) of (A,B2).
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-rand('seed',0);nx=6;nz=3;nu=2;ny=1;
-A=diag(1:6);A(2,2)=-7;A(5,5)=-9;B2=[1,2;0,3;0,4;0,5;0,0;0,0];
-C1=[zeros(nz,nz),eye(nz,nz)];D12=[0,1;0,2;0,3];
-Sys12=syslin('c',A,B2,C1,D12);
-C=[C1;rand(ny,nx)];D2=[D12;rand(ny,size(D12,2))];
-Sys=syslin('c',A,B2,C,D2);
-[A,B2,C1,D12]=abcd(Sys12);  //The matrices of Sys12.
-my_alpha=-1;my_beta=-2;flag='ge';
-[X,dims,F,U,k,Z]=abinv(Sys12,my_alpha,my_beta,flag);
-clean(X'*(A+B2*F)*X)
-clean(X'*B2*U)
-clean((C1+D12*F)*X)
-clean(D12*U);
-//Calculating an ad-hoc B1,D1
-G1=rand(size(B2,2),3);
-B1=-B2*G1;
-D11=-D12*G1;
-D1=[D11;rand(ny,size(B1,2))];
-
-[Closed,F,G]=ddp(Sys,1:nz,B1,D1,'st',my_alpha,my_beta);
-closed=syslin('c',A+B2*F,B1+B2*G,C1+D12*F,D11+D12*G);
-ss2tf(closed)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="abinv">abinv</link>
-            </member>
-            <member>
-                <link linkend="ui_observer">ui_observer</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/ccontrg.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/ccontrg.xml
deleted file mode 100644 (file)
index 02e3381..0000000
+++ /dev/null
@@ -1,101 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - P. Gahinet
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="ccontrg">
-    <refnamediv>
-        <refname>ccontrg</refname>
-        <refpurpose>Central H-infinity continuous time controller</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[K]=ccontrg(P,r,gamma);</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para> a continuous time linear dynamical system in state-space representation.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        a two elements vector with integer values: the dimension of the 2,2 part of <literal>P</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>gamma</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            returns a realization <literal>K</literal> of the central controller for the
-            general standard problem in state-space form.
-        </para>
-        <para>
-            <note>
-                Note that gamma must be &gt; gopt (output of <literal>gamitg</literal>)
-            </note>
-        </para>
-        <para>
-            P contains the parameters of plant realization <literal>(A,B,C,D)</literal>
-            (<literal>syslin</literal> list) with
-        </para>
-        <programlisting role=""><![CDATA[
-B = ( B1 , B2 ) ,        C= ( C1 ) ,    D = ( D11  D12)
-                            ( C2 )          ( D21  D22)
- ]]></programlisting>
-        <para>
-            <literal>r(1)</literal> and <literal>r(2)</literal> are the
-            dimensions of <literal>D22</literal> (rows x columns)
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="gamitg">gamitg</link>
-            </member>
-            <member>
-                <link linkend="h_inf">h_inf</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Authors</title>
-        <para>P. Gahinet (INRIA);   </para>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for continuous time linear dynamical system.
-                    This modification has been introduced by this  <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/dhinf.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/dhinf.xml
deleted file mode 100644 (file)
index b14012f..0000000
+++ /dev/null
@@ -1,232 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="dhinf">
-    <refnamediv>
-        <refname>dhinf</refname>
-        <refpurpose>H_infinity design of discrete-time systems</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[AK,BK,CK,DK,(RCOND)] = dishin(A,B,C,D,ncon,nmeas,gamma)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>the n-by-n system state matrix A.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>B</term>
-                <listitem>
-                    <para>the n-by-m system input matrix B.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>C</term>
-                <listitem>
-                    <para>the p-by-n system output matrix C.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>D</term>
-                <listitem>
-                    <para>the p-by-m system matrix D.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>ncon</term>
-                <listitem>
-                    <para>the number of control inputs. m &gt;= ncon &gt;= 0, p-nmeas &gt;= ncon.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>nmeas</term>
-                <listitem>
-                    <para>the number of measurements. p &gt;= nmeas &gt;= 0, m-ncon &gt;= nmeas.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>gamma</term>
-                <listitem>
-                    <para>
-                        the parameter gamma used in <literal>H_infinity</literal> design. It is assumed that gamma is sufficiently large so that the controller is admissible. gamma &gt;= 0.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>AK</term>
-                <listitem>
-                    <para>the n-by-n controller state matrix AK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>BK</term>
-                <listitem>
-                    <para>the n-by-nmeas controller input matrix BK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>CK</term>
-                <listitem>
-                    <para>the ncon-by-n controller output matrix CK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>DK</term>
-                <listitem>
-                    <para>the ncon-by-nmeas controller matrix DK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>RCOND</term>
-                <listitem>
-                    <para>a vector containing estimates of the reciprocal condition numbers of the matrices which are to be inverted and estimates of the reciprocal condition numbers of the Riccati equations which have to be solved during the computation of the controller. (See the description of the algorithm in [1].)</para>
-                    <variablelist>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(1) contains the reciprocal condition number of the  matrix R3,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(2) contains the reciprocal condition number of the  matrix R1 - R2'*inv(R3)*R2</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(3) contains the reciprocal condition number of the matrix V21,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(4) contains the reciprocal condition number of the   matrix St3,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(5) contains the reciprocal condition number of the  matrix V12,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(6) contains the reciprocal condition number of the matrix Im2 + DKHAT*D22,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(7) contains the reciprocal condition number of the  X-Riccati equation,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(8) contains the reciprocal condition number of the  Z-Riccati equation.</para>
-                            </listitem>
-                        </varlistentry>
-                    </variablelist>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[AK,BK,CK,DK,(RCOND)] = dhinf(A,B,C,D,ncon,nmeas, gamma)</literal>
-            To compute the matrices of an H-infinity (sub)optimal n-state
-            controller
-        </para>
-        <programlisting role=""><![CDATA[
-    | AK | BK |
-K = |----|----|,
-    | CK | DK |
- ]]></programlisting>
-        <para>
-            for the discrete-time system
-        </para>
-        <programlisting role=""><![CDATA[
-    | A  | B1  B2  |   | A | B |
-P = |----|---------| = |---|---|,
-    | C1 | D11 D12 |   | C | D |
-    | C2 | D21 D22 |
- ]]></programlisting>
-        <para>
-            and for a given value of gamma, where B2 has column size of the
-            number of control inputs (ncon) and C2 has row size of the number
-            of measurements (nmeas) being provided to the controller.
-        </para>
-    </refsection>
-    <refsection>
-        <title>References</title>
-        <para>
-            [1] P.Hr. Petkov, D.W. Gu and M.M. Konstantinov. Fortran 77 routines        for Hinf and H2 design of linear discrete-time control systems.        Report99-8, Department of Engineering, Leicester University,        April 1999.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-//example from Niconet report SLWN1999-12
-//Hinf
-A=[-0.7  0    0.3  0   -0.5 -0.1
-   -0.6  0.2 -0.4 -0.3  0    0
-   -0.5  0.7 -0.1  0    0   -0.8
-   -0.7  0    0   -0.5 -1    0
-    0    0.3  0.6 -0.9  0.1 -0.4
-    0.5 -0.8  0    0    0.2 -0.9];
-B=[-1 -2 -2  1  0
-    1  0  1 -2  1
-   -3 -4  0  2 -2
-    1 -2  1  0 -1
-    0  1 -2  0  3
-    1  0  3 -1 -2];
-C=[ 1 -1  2 -2  0 -3
-   -3  0  1 -1  1  0
-    0  2  0 -4  0 -2
-    1 -3  0  0  3  1
-    0  1 -2  1  0 -2];
-D=[1 -1 -2  0  0
-   0  1  0  1  0
-   2 -1 -3  0  1
-   0  1  0  1 -1
-   0  0  1  2  1];
-
-ncon=2
-nmeas=2
-gam=111.30;
-[AK,BK,CK,DK] = dhinf(A,B,C,D,ncon,nmeas,gam)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="hinf">hinf</link>
-            </member>
-            <member>
-                <link linkend="h_inf">h_inf</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/dhnorm.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/dhnorm.xml
deleted file mode 100644 (file)
index f17095b..0000000
+++ /dev/null
@@ -1,80 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="dhnorm">
-    <refnamediv>
-        <refname>dhnorm</refname>
-        <refpurpose>discrete H-infinity norm</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>hinfnorm=dhnorm(sl,[tol],[normax])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>sl</term>
-                <listitem>
-                    <para>
-                        the state space system (<literal>syslin</literal> list) (discrete-time)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>
-                        tolerance in bisection step, default value <literal>0.01</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>normax</term>
-                <listitem>
-                    <para>
-                        upper bound for the norm , default value is <literal>1000</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>hinfnorm</term>
-                <listitem>
-                    <para>
-                        the discrete infinity norm of <literal>Sl</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            produces the discrete-time infinity norm  of a state-space system
-            (the maximum over all frequencies on the unit circle of the maximum singular value).
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="h_norm">h_norm</link>
-            </member>
-            <member>
-                <link linkend="linfn">linfn</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/gamitg.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/gamitg.xml
deleted file mode 100644 (file)
index 99d359b..0000000
+++ /dev/null
@@ -1,115 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="gamitg">
-    <refnamediv>
-        <refname>gamitg</refname>
-        <refpurpose>H-infinity gamma iterations for continuous time systems</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[gopt]=gamitg(G,r,prec [,options]);</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>G</term>
-                <listitem>
-                    <para>a continuous time dynamical system (plant realization).</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 row vector (dimension of <literal>G22</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>prec</term>
-                <listitem>
-                    <para>desired relative accuracy on the norm</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>option</term>
-                <listitem>
-                    <para>
-                        string <literal>'t'</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>gopt</term>
-                <listitem>
-                    <para>real scalar, optimal H-infinity gain</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>gopt=gamitg(G,r,prec [,options])</literal>
-            returns the H-infinity optimal gain <literal>gopt</literal>.
-        </para>
-        <para>
-            <literal>G</literal> contains the state-space matrices <literal>[A,B,C,D]</literal> of
-            the plant with the usual partitions:
-        </para>
-        <programlisting role=""><![CDATA[
-B = ( B1 , B2 ) ,    C = ( C1 ) ,    D = ( D11  D12)
-                         ( C2 )          ( D21  D22)
- ]]></programlisting>
-        <para>
-            These partitions are implicitly given in <literal>r</literal>: <literal>r(1)</literal>
-            and <literal>r(2)</literal> are the dimensions of <literal>D22</literal> (rows x columns)
-        </para>
-        <para>
-            With <literal>option='t'</literal>, <literal>gamitg</literal> traces each bisection step, i.e.,
-            displays the lower and upper bounds and the current test point.
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="ccontrg">ccontrg</link>
-            </member>
-            <member>
-                <link linkend="h_inf">h_inf</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Authors</title>
-        <para>P. Gahinet</para>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h2norm.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h2norm.xml
deleted file mode 100644 (file)
index 8174c43..0000000
+++ /dev/null
@@ -1,72 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="h2norm">
-    <refnamediv>
-        <refname>h2norm</refname>
-        <refpurpose>H2 norm of a continuous time proper dynamical system</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[n]=h2norm(Sl [,tol])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sl</term>
-                <listitem>
-                    <para>continuous time proper linear dynamical system</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>n</term>
-                <listitem>
-                    <para>real scalar</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            produces the H2 norm  of a linear continuous time system <literal>Sl</literal>.
-        </para>
-        <para>
-            (For <literal>Sl</literal> in state-space form <literal>h2norm</literal> uses the observability
-            gramian and for <literal>Sl</literal> in transfer form <literal>h2norm</literal> uses a residue method)
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-    h=syslin('c',(2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01));
-    h2norm(h)
-    ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_cl.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_cl.xml
deleted file mode 100644 (file)
index 8b48bfa..0000000
+++ /dev/null
@@ -1,98 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - F. Delebecque
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="h_cl">
-    <refnamediv>
-        <refname>h_cl</refname>
-        <refpurpose>closed loop matrix</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[Acl]=h_cl(P,r,K)
-            [Acl]=h_cl(P22,K)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P, P22</term>
-                <listitem>
-                    <para>continuous time linear dynamical systems: augmented plant or nominal plant respectively</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        a two elements vector, dimensions of 2,2 part of <literal>P</literal> (<literal>r=[rows,cols]=size(P22)</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K</term>
-                <listitem>
-                    <para>a continuous time linear dynamical system: the controller</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Acl</term>
-                <listitem>
-                    <para>real square matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Given the standard plant <literal>P</literal> (with <literal>r=size(P22)</literal>) and the controller
-            <literal>K</literal>, this function returns the closed loop matrix <literal>Acl</literal>.
-        </para>
-        <para>
-            The poles of <literal>Acl</literal> must be stable for the internal stability
-            of the closed loop system.
-        </para>
-        <para>
-            <literal>Acl</literal> is the <literal>A</literal>-matrix of the linear system <literal>[I -P22;-K I]^-1</literal> i.e.
-            the <literal>A</literal>-matrix of <literal>lft(P,r,K)</literal>
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lft">lft</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Authors</title>
-        <para>F. D.  </para>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_inf.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_inf.xml
deleted file mode 100644 (file)
index 65674cc..0000000
+++ /dev/null
@@ -1,139 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - F. Delebecque
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="h_inf">
-    <refnamediv>
-        <refname>h_inf</refname>
-        <refpurpose>Continuous time H-infinity (central) controller</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[Sk,ro]=h_inf(P,r,romin,romax,nmax)
-            [Sk,rk,ro]=h_inf(P,r,romin,romax,nmax)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>a continuous-time linear dynamical system ("augmented" plant given in state-space form  or in transfer form)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        size of the <literal>P22</literal> plant i.e. 2-vector <literal>[#outputs,#inputs]</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>romin,romax</term>
-                <listitem>
-                    <para>
-                        a priori bounds on <literal>ro</literal> with <literal>ro=1/gama^2</literal>; (<literal>romin=0</literal>  usually)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>nmax</term>
-                <listitem>
-                    <para>integer, maximum number of iterations in the gama-iteration.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>h_inf</literal> computes H-infinity optimal controller for the
-            continuous-time plant <literal>P</literal>.
-        </para>
-        <para>
-            The partition of <literal>P</literal> into four sub-plants is given through
-            the 2-vector <literal>r</literal> which is the size of the <literal>22</literal> part of <literal>P</literal>.
-        </para>
-        <para>
-            <literal>P</literal> is given in state-space
-            e.g. <literal>P=syslin('c',A,B,C,D)</literal> with <literal>A,B,C,D</literal> = constant matrices
-            or <literal>P=syslin('c',H)</literal> with <literal>H</literal> a transfer matrix.
-        </para>
-        <para>
-            <literal>[Sk,ro]=H_inf(P,r,romin,romax,nmax)</literal> returns
-            <literal>ro</literal> in <literal>[romin,romax]</literal> and the central
-            controller <literal>Sk</literal> in the same representation as
-            <literal>P</literal>.
-        </para>
-        <para>
-            (All calculations are made in state-space, i.e conversion to
-            state-space is done by the function, if necessary).
-        </para>
-        <para>
-            Invoked with three LHS parameters,
-        </para>
-        <para>
-            <literal>[Sk,rk,ro]=H_inf(P,r,romin,romax,nmax)</literal> returns
-            <literal>ro</literal> and the Parameterization of all stabilizing
-            controllers:
-        </para>
-        <para>
-            a stabilizing controller <literal>K</literal> is obtained by
-            <literal>K=lft(Sk,r,PHI)</literal> where <literal>PHI</literal> is a linear
-            system with dimensions <literal>r'</literal> and satisfy:
-        </para>
-        <para>
-            <literal>H_norm(PHI) &lt; gamma</literal>.  <literal>rk (=r)</literal> is the
-            size of the <literal>Sk22</literal> block and <literal>ro = 1/gama^2</literal>
-            after <literal>nmax</literal> iterations.
-        </para>
-        <para>
-            Algorithm is adapted from Safonov-Limebeer. Note that <literal>P</literal> is assumed to be
-            a continuous-time plant.
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="gamitg">gamitg</link>
-            </member>
-            <member>
-                <link linkend="ccontrg">ccontrg</link>
-            </member>
-            <member>
-                <link linkend="leqr">leqr</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>Authors</title>
-        <para>F.Delebecque INRIA (1990)  </para>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_inf_st.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_inf_st.xml
deleted file mode 100644 (file)
index eb4affe..0000000
+++ /dev/null
@@ -1,62 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - F. Delebecque
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="h_inf_st">
-    <refnamediv>
-        <refname>h_inf_st</refname>
-        <refpurpose>static H_infinity problem</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[Kopt,gamaopt]=h_inf_stat(D,r)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>D</term>
-                <listitem>
-                    <para>real matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>1x2 vector</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Kopt</term>
-                <listitem>
-                    <para>matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            computes a matrix <literal>Kopt</literal> such that largest singular value of:
-        </para>
-        <para>
-            <literal>lft(D,r,K)=D11+D12* K*inv(I-D22*K)* D21</literal>
-            is minimal (Static <literal>H_infinity</literal> four blocks problem).
-        </para>
-        <para>
-            D is partionned as <literal>D=[D11 D12; D21 D22]</literal>
-            where <literal>size(D22)=r=[r1 r2]</literal>
-        </para>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_norm.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/h_norm.xml
deleted file mode 100644 (file)
index f605b5e..0000000
+++ /dev/null
@@ -1,81 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="h_norm">
-    <refnamediv>
-        <refname>h_norm</refname>
-        <refpurpose>H-infinity norm</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[hinfnorm [,frequency]]=h_norm(sl [,rerr])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>sl</term>
-                <listitem>
-                    <para>
-                        the state space system (<literal>syslin</literal> list)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rerr</term>
-                <listitem>
-                    <para>
-                        max. relative error, default value <literal>1e-8</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>hinfnorm</term>
-                <listitem>
-                    <para>
-                        the infinity norm of <literal>Sl</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>frequency</term>
-                <listitem>
-                    <para>frequency at which maximum is achieved</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            produces the infinity norm  of a state-space system
-            (the maximum over all frequencies of the maximum singular value).
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="linfn">linfn</link>
-            </member>
-            <member>
-                <link linkend="linf">linf</link>
-            </member>
-            <member>
-                <link linkend="svplot">svplot</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/hinf.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/hinf.xml
deleted file mode 100644 (file)
index a1681d5..0000000
+++ /dev/null
@@ -1,206 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="hinf">
-    <refnamediv>
-        <refname>hinf</refname>
-        <refpurpose>H_infinity design of continuous-time systems</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[AK,BK,CK,DK,(RCOND)] = hinf(A,B,C,D,ncon,nmeas,gamma)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>the n-by-n system state matrix A.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>B</term>
-                <listitem>
-                    <para>the n-by-m system input matrix B.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>C</term>
-                <listitem>
-                    <para>the p-by-n system output matrix C.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>D</term>
-                <listitem>
-                    <para>the p-by-m system matrix D.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>ncon</term>
-                <listitem>
-                    <para>the number of control inputs. m &gt;= ncon &gt;= 0, p-nmeas &gt;= ncon.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>nmeas</term>
-                <listitem>
-                    <para>the number of measurements. p &gt;= nmeas &gt;= 0, m-ncon &gt;= nmeas.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>gamma</term>
-                <listitem>
-                    <para>
-                        the parameter gamma used in <literal>H_infinity</literal> design.
-                        It is assumed that gamma is sufficiently large so that the controller is admissible. gamma &gt;= 0.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>AK</term>
-                <listitem>
-                    <para>the n-by-n controller state matrix AK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>BK</term>
-                <listitem>
-                    <para>the n-by-nmeas controller input matrix BK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>CK</term>
-                <listitem>
-                    <para>the ncon-by-n controller output matrix CK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>DK</term>
-                <listitem>
-                    <para>the ncon-by-nmeas controller matrix DK.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>RCOND</term>
-                <listitem>
-                    <para>a vector containing estimates of the reciprocal condition numbers of the matrices which are to be inverted and estimates of the reciprocal condition numbers of the Riccati equations which have to be solved during the computation of the controller. (See the description of the algorithm in [1].)</para>
-                    <variablelist>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(1) contains the reciprocal condition number of the  control transformation matrix TU,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(2) contains the reciprocal condition number of the  measurement transformation matrix TY,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(3) contains an estimate of the reciprocal condition number of the X-Riccati equation,</para>
-                            </listitem>
-                        </varlistentry>
-                        <varlistentry>
-                            <term>RCOND</term>
-                            <listitem>
-                                <para>(4) contains an estimate of the reciprocal condition number of the Y-Riccati equation.</para>
-                            </listitem>
-                        </varlistentry>
-                    </variablelist>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[AK,BK,CK,DK,(RCOND)] = hinf(A,B,C,D,ncon,nmeas,gamma)</literal>
-            To compute the matrices of an H-infinity (sub)optimal n-state
-            controller
-        </para>
-        <programlisting role=""><![CDATA[
-    | AK | BK |
-K = |----|----|,
-    | CK | DK |
- ]]></programlisting>
-        <para>
-            for the continuous-time system
-        </para>
-        <programlisting role=""><![CDATA[
-    | A  | B1  B2  |   | A | B |
-P = |----|---------| = |---|---|,
-    | C1 | D11 D12 |   | C | D |
-    | C2 | D21 D22 |
- ]]></programlisting>
-        <para>
-            and for a given value of gamma, where B2 has column size of the
-            number of control inputs (ncon) and C2 has row size of the number
-            of measurements (nmeas) being provided to the controller.
-        </para>
-    </refsection>
-    <refsection>
-        <title>References</title>
-        <para>
-            [1] P.Hr. Petkov, D.W. Gu and M.M. Konstantinov. Fortran 77 routines     for Hinf and H2 design of continuous-time linear control systems.     Report98-14, Department of Engineering, Leicester University,     August 1998.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-//example from Niconet report SLWN1999-12
-//Hinf
-A=[-1  0  4  5 -3 -2
-   -2  4 -7 -2  0  3
-   -6  9 -5  0  2 -1
-   -8  4  7 -1 -3  0
-    2  5  8 -9  1 -4
-    3 -5  8  0  2 -6];
-
-B=[-3 -4 -2  1  0
-    2  0  1 -5  2
-   -5 -7  0  7 -2
-    4 -6  1  1 -2
-   -3  9 -8  0  5
-    1 -2  3 -6 -2];
-
-C=[ 1 -1  2 -4  0 -3
-   -3  0  5 -1  1  1
-   -7  5  0 -8  2 -2
-    9 -3  4  0  3  7
-    0  1 -2  1 -6 -2];
-
-D=[ 1 -2 -3  0  0
-    0  4  0  1  0
-    5 -3 -4  0  1
-    0  1  0  1 -3
-    0  0  1  7  1];
-Gamma=10.18425636157899;
-[AK,BK,CK,DK] = hinf(A,B,C,D,2,2,Gamma)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="dhinf">dhinf</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/linf.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/linf.xml
deleted file mode 100644 (file)
index c07ab38..0000000
+++ /dev/null
@@ -1,74 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="linf">
-    <refnamediv>
-        <refname>linf</refname>
-        <refpurpose>infinity norm</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>linf(g [,eps],[tol])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>g</term>
-                <listitem>
-                    <para>
-                        is a <literal>syslin</literal> linear system.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>eps</term>
-                <listitem>
-                    <para>is error tolerance on n.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>threshold for imaginary axis poles.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            returns the L_infinity norm of <literal>g</literal>.
-        </para>
-        <programlisting role=""><![CDATA[
-n=sup [sigmax(g(jw)]
-   w
- ]]></programlisting>
-        <para>
-            (sigmax largest singular value).
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="h_norm">h_norm</link>
-            </member>
-            <member>
-                <link linkend="linfn">linfn</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/linfn.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/linfn.xml
deleted file mode 100644 (file)
index 1976c26..0000000
+++ /dev/null
@@ -1,123 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - P. Gahinet
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="linfn">
-    <refnamediv>
-        <refname>linfn</refname>
-        <refpurpose>infinity norm</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[x,freq]=linfn(G,PREC,RELTOL,options);</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>G</term>
-                <listitem>
-                    <para>
-                        is a <literal>syslin</literal> list
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>PREC</term>
-                <listitem>
-                    <para>desired relative accuracy on the norm</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>RELTOL</term>
-                <listitem>
-                    <para>relative threshold to decide when an eigenvalue can be  considered on the imaginary axis.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>options</term>
-                <listitem>
-                    <para>
-                        available options are <literal>'trace'</literal> or <literal>'cond'</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>x</term>
-                <listitem>
-                    <para>is the computed norm.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>freq</term>
-                <listitem>
-                    <para>vector</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Computes the Linf (or Hinf) norm of <literal>G</literal>
-            This norm is well-defined as soon as the realization
-            <literal>G=(A,B,C,D)</literal> has no imaginary eigenvalue which is both
-            controllable and observable.
-        </para>
-        <para>
-            <literal>freq</literal> is a list of the frequencies for which <literal>||G||</literal> is
-            attained,i.e., such that <literal>||G (j om)|| = ||G||</literal>.
-        </para>
-        <para>
-            If -1 is in the list, the norm is attained at infinity.
-        </para>
-        <para>
-            If -2 is in the list, <literal>G</literal> is all-pass in some direction so that
-            <literal>||G (j omega)|| = ||G||</literal> for all frequencies omega.
-        </para>
-        <para>
-            The algorithm follows the paper by G. Robel
-            (AC-34 pp. 882-884, 1989).
-            The case <literal>D=0</literal> is not treated separately due to superior
-            accuracy of the general method when <literal>(A,B,C)</literal> is nearly
-            non minimal.
-        </para>
-        <para>
-            The <literal>'trace'</literal> option traces each bisection step, i.e., displays
-            the lower and upper bounds and the current test point.
-        </para>
-        <para>
-            The <literal>'cond'</literal> option estimates a confidence index on the computed
-            value and issues a warning if computations are
-            ill-conditioned
-        </para>
-        <para>
-            In the general case (<literal>A</literal> neither stable nor anti-stable),
-            no upper bound is  prespecified.
-        </para>
-        <para>
-            If by contrast <literal>A</literal> is stable or anti stable, lower
-            and upper bounds are computed using the associated
-            Lyapunov solutions.
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="h_norm">h_norm</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/macglov.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/macglov.xml
deleted file mode 100644 (file)
index 02c9fc6..0000000
+++ /dev/null
@@ -1,97 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="macglov">
-    <refnamediv>
-        <refname>macglov</refname>
-        <refpurpose>Continuous time dynamical systems Mac Farlane Glover problem</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[P,r]=macglov(Sl)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sl</term>
-                <listitem>
-                    <para>a continuous time linear dynamical system</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>a continuous time linear dynamical system, the "augmented" plant</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 vector, dimension of <literal>P22</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[P,r]=macglov(Sl)</literal> returns the standard plant
-            <literal>P</literal> for the Glover-McFarlane problem.
-        </para>
-        <para>
-            For this problem <literal>ro_optimal = 1-hankel_norm([N,M]</literal>)
-            with <literal>[N,M]=lcf(sl)</literal> (Normalized coprime factorization) i.e.
-        </para>
-        <para>
-            <literal>gama_optimal = 1/sqrt(ro_optimal)</literal>
-        </para>
-        <para>
-            <literal>P</literal> is returned in the same
-            representation (transfer function or state-space) than
-            <literal>Sl</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        MAC-FARLANE PROBLEM for G=1/s^3;
-        <programlisting role="example"><![CDATA[
-    G=syslin("c",1/%s^3);
-    [P,r]=macglov(G);
-
-    //K Optimal controller , ro = gamaopt^-2;
-    [K,ro]=h_inf(P,r,0,1,30);
-
-    ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>Authors</title>
-        <para>F. Delebecque INRIA</para>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for continuous time linear dynamical system.
-                    This modification has been introduced by this  <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/nehari.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/nehari.xml
deleted file mode 100644 (file)
index b276251..0000000
+++ /dev/null
@@ -1,78 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="nehari">
-    <refnamediv>
-        <refname>nehari</refname>
-        <refpurpose>Nehari approximant of continuous time dynamical systems</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[x]=nehari(R [,tol])</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>R</term>
-                <listitem>
-                    <para>a continuous time linear dynamical system in state-space representation.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>x</term>
-                <listitem>
-                    <para>a continuous time linear dynamical system in state-space representation.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>optional threshold, default value is 1e-6.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>[x]=nehari(R [,tol])returns</literal> the Nehari approximant of <literal>R</literal>.
-        </para>
-        <para>
-            <literal>R</literal> = linear system in state-space representation (<literal>syslin</literal> list).
-        </para>
-        <para>
-            <literal>R</literal> is strictly proper and <literal>- R~</literal> is stable
-            (i.e. <literal>R</literal> is anti stable).
-        </para>
-        <programlisting role="no-scilab-exec"><![CDATA[
-|| R - X ||oo = min || R - Y ||oo
-              Y in Hoo
- ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/parrot.xml b/scilab/modules/cacsd/help/fr_FR/control_design/h_infinity/parrot.xml
deleted file mode 100644 (file)
index 348d73b..0000000
+++ /dev/null
@@ -1,62 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="parrot">
-    <refnamediv>
-        <refname>parrot</refname>
-        <refpurpose>Parrot's problem</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>K=parrot(D,r)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>D,K</term>
-                <listitem>
-                    <para>matrices</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1X2 vector (dimension of the 2,2 part of <literal>D</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Given a matrix <literal>D</literal> partionned as <literal>[D11 D12; D21 D22]</literal>
-            where <literal>size(D22)=r=[r1,r2]</literal>
-            compute a matrix <literal>K</literal> such that
-            largest singular value of <literal>[D11 D12; D21 D22+K]</literal>
-            is minimal (Parrot's problem)
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="h_inf_st">h_inf_st</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/fourplan.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/fourplan.xml
deleted file mode 100644 (file)
index 9c8c8b0..0000000
+++ /dev/null
@@ -1,90 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="fourplan">
-    <refnamediv>
-        <refname>fourplan</refname>
-        <refpurpose>augmented plant to four plants</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[P11,P12,P21,P22]=fourplan(P,r)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list (linear system)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 row vector, dimension of <literal>P22</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>P11,P12,P21,P22</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> lists.
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Utility function.
-        </para>
-        <para>
-            <literal>P</literal> being partitioned as follows:
-        </para>
-        <programlisting role=""><![CDATA[
-P=[ P11 P12;
-    P21 P22]
- ]]></programlisting>
-        <para>
-            with <literal>size(P22)=r</literal> this function returns the four linear systems <literal>P11,P12,P21,P22</literal>.
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqg">lqg</link>
-            </member>
-            <member>
-                <link linkend="lqg2stan">lqg2stan</link>
-            </member>
-            <member>
-                <link linkend="lqr">lqr</link>
-            </member>
-            <member>
-                <link linkend="lqe">lqe</link>
-            </member>
-            <member>
-                <link linkend="lft">lft</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/gcare.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/gcare.xml
deleted file mode 100644 (file)
index 0f807f2..0000000
+++ /dev/null
@@ -1,86 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="gcare">
-    <refnamediv>
-        <refname>gcare</refname>
-        <refpurpose>Continuous time control Riccati equation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[X,F]=gcare(Sl)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sl</term>
-                <listitem>
-                    <para>a continuous time linear dynamical system in state-space representation</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>X</term>
-                <listitem>
-                    <para>symmetric matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>F</term>
-                <listitem>
-                    <para>real matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Generalized Control Algebraic Riccati Equation (GCARE).
-            <literal>X</literal> = solution , <literal>F</literal> = gain.
-        </para>
-        <para>
-            The GCARE for <literal>Sl=[A,B,C,D]</literal> is:
-        </para>
-        <programlisting role=""><![CDATA[
-(A-B*Si*D'*C)'*X+X*(A-B*Si*D'*C)-X*B*Si*B'*X+C'*Ri*C=0
- ]]></programlisting>
-        <para>
-            where <literal>S=(eye()+D'*D)</literal>, <literal>Si=inv(S)</literal>, <literal>R=(eye()+D*D')</literal>, <literal>Ri=inv(R)</literal>
-            and <literal>F=-Si*(D'*C+B'*X)</literal> is such that <literal>A+B*F</literal> is stable.
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="gfare">gfare</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/gfare.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/gfare.xml
deleted file mode 100644 (file)
index 13d35d9..0000000
+++ /dev/null
@@ -1,86 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="gfare">
-    <refnamediv>
-        <refname>gfare</refname>
-        <refpurpose>Continuous time filter Riccati equation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[Z,H]=gfare(Sl)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sl</term>
-                <listitem>
-                    <para>a continuous time linear dynamical system in state-space representation</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Z</term>
-                <listitem>
-                    <para>symmetric matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>H</term>
-                <listitem>
-                    <para>real matrix</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Generalized Filter Algebraic Riccati Equation (GFARE).
-            <literal>Z</literal> = solution, <literal>H</literal> = gain.
-        </para>
-        <para>
-            The GFARE for <literal>Sl=[A,B,C,D]</literal> is:
-        </para>
-        <programlisting role=""><![CDATA[
-(A-B*D'*Ri*C)*Z+Z*(A-B*D'*Ri*C)'-Z*C'*Ri*C*Z+B*Si*B'=0
- ]]></programlisting>
-        <para>
-            where <literal>S=(eye()+D'*D)</literal>, <literal>Si=inv(S)</literal>, <literal>R=(eye()+D*D')</literal>, <literal>Ri=inv(R)</literal>
-            and <literal>H=-(B*D'+Z*C')*Ri</literal> is such that <literal>A+H*C</literal> is stable.
-        </para>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="gcare">gcare</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/leqr.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/leqr.xml
deleted file mode 100644 (file)
index 40ebbb3..0000000
+++ /dev/null
@@ -1,119 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - F. Delebecque
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="leqr">
-    <refnamediv>
-        <refname>leqr</refname>
-        <refpurpose>H-infinity LQ gain (full state)  </refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[K,X,err]=leqr(P12,Vx)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P12</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Vx</term>
-                <listitem>
-                    <para>symmetric nonnegative matrix (should be small enough)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K,X</term>
-                <listitem>
-                    <para>two real matrices</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>err</term>
-                <listitem>
-                    <para>a real number (l1 norm of LHS of Riccati equation)</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>leqr</literal>  computes the linear suboptimal H-infinity LQ full-state gain
-            for the plant <literal>P12=[A,B2,C1,D12]</literal> in continuous or discrete time.
-        </para>
-        <para>
-            <literal>P12</literal> is a <literal>syslin</literal> list (e.g. <literal>P12=syslin('c',A,B2,C1,D12)</literal>).
-        </para>
-        <programlisting role=""><![CDATA[
-[C1' ]               [Q  S]
-[    ]  * [C1 D12] = [    ]
-[D12']               [S' R]
- ]]></programlisting>
-        <para>
-            <literal>Vx</literal> is related to the variance matrix of the noise <literal>w</literal> perturbing <literal>x</literal>;
-            (usually <literal>Vx=gama^-2*B1*B1'</literal>).
-        </para>
-        <para>
-            The gain <literal>K</literal> is such that <literal>A + B2*K</literal> is stable.
-        </para>
-        <para>
-            <literal>X</literal> is the stabilizing solution of the Riccati equation.
-        </para>
-        <para>
-            For a continuous plant:
-        </para>
-        <programlisting role=""><![CDATA[
-(A-B2*inv(R)*S')'*X+X*(A-B2*inv(R)*S')-X*(B2*inv(R)*B2'-Vx)*X+Q-S*inv(R)*S'=0
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-inv(R)*(B2'*X+S)
- ]]></programlisting>
-        <para>
-            For a discrete time plant:
-        </para>
-        <programlisting role=""><![CDATA[
-X-(Abar'*inv((inv(X)+B2*inv(R)*B2'-Vx))*Abar+Qbar=0
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-inv(R)*(B2'*inv(inv(X)+B2*inv(R)*B2'-Vx)*Abar+S')
- ]]></programlisting>
-        <para>
-            with <literal>Abar=A-B2*inv(R)*S'</literal> and <literal>Qbar=Q-S*inv(R)*S'</literal>
-        </para>
-        <para>
-            The 3-blocks matrix pencils associated with these Riccati equations are:
-        </para>
-        <programlisting role=""><![CDATA[
-             discrete                        continuous
- |I  -Vx  0|   | A    0    B2|       |I   0   0|   | A    Vx    B2|
-z|0   A'  0| - |-Q    I    -S|      s|0   I   0| - |-Q   -A'   -S |
- |0   B2' 0|   | S'   0     R|       |0   0   0|   | S'   -B2'   R|
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqr">lqr</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqe.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqe.xml
deleted file mode 100644 (file)
index 5e933f7..0000000
+++ /dev/null
@@ -1,150 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - F. Delebecque
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lqe">
-    <refnamediv>
-        <refname>lqe</refname>
-        <refpurpose>linear quadratic estimator (Kalman Filter)  </refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[K,X]=lqe(P21)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P21</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K, X</term>
-                <listitem>
-                    <para>real matrices</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>lqe</literal> returns the Kalman gain for the filtering
-            problem in continuous or discrete time.
-        </para>
-        <para>
-            <literal>P21</literal> is a <literal>syslin</literal> list representing the system <literal>P21=[A,B1,C2,D21] P21=syslin('c',A,B1,C2,D21) or P21=syslin('d',A,B1,C2,D21)</literal>
-        </para>
-        <para>
-            The input to <literal>P21</literal> is a white noise with variance:
-        </para>
-        <programlisting role=""><![CDATA[
-     [B1 ]               [Q  S]
-BigV=[   ] [ B1' D21'] = [    ]
-     [D21]               [S' R]
- ]]></programlisting>
-        <para>
-            <literal>X</literal> is the solution of the stabilizing Riccati
-            equation and <literal>A+K*C2</literal> is stable.
-        </para>
-        <para>
-            In continuous time:
-        </para>
-        <programlisting role=""><![CDATA[
-(A-S*inv(R)*C2)*X+X*(A-S*inv(R)*C2)'-X*C2'*inv(R)*C2*X+Q-S*inv(R)*S'=0
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-(X*C2'+S)*inv(R)
- ]]></programlisting>
-        <para>
-            In discrete time:
-        </para>
-        <programlisting role=""><![CDATA[
-X=A*X*A'-(A*X*C2'+B1*D21')*pinv(C2*X*C2'+D21*D21')*(C2*X*A'+D21*B1')+B1*B1'
- ]]></programlisting>
-        <para>
-            <literal>K=-(A*X*C2'+B1*D21')*pinv(C2*X*C2'+D21*D21')</literal>
-        </para>
-        <para>
-            <literal>xhat(t+1)= E(x(t+1)| y(0),...,y(t))</literal> (one-step predicted <literal>x</literal>)
-            satisfies the recursion:
-        </para>
-        <programlisting role=""><![CDATA[
-xhat(t+1)=(A+K*C2)*xhat(t) - K*y(t).
- ]]></programlisting>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-//Assume the equations
-//.
-//x = Ax + Ge
-//y = Cx + v
-//with
-//E ee' = Q_e,    Evv' = R,    Eev' = N
-//
-//This is equivalent to
-//.
-//x = Ax  + B1 w
-//y = C2x + D21 w
-//with E { [Ge ]  [Ge v]' } = E { [B1w ] [B1w D21w]' } = bigR =
-//         [ v ]                  [D21w]
-//
-//[B1*B1'  B1*D21';
-// D21*B1'  D21*D21']
-//=
-//[G*Q_e*G' G*N;
-// N*G' R]
-
-//To find (B1,D21) given (G,Q_e,R,N) form bigR =[G*Q_e*G' G*N;N'*G' R].
-//Then [W,Wt]=fullrf(bigR);  B1=W(1:size(G,1),:);
-//D21=W(($+1-size(C2,1)):$,:)
-//
-//P21=syslin('c',A,B1,C2,D21);
-//[K,X]=lqe(P21);
-
-//Example:
-nx=5;ne=2;ny=3;
-A=-diag(1:nx);G=ones(nx,ne);
-C=ones(ny,nx); Q_e(ne,ne)=1; R=diag(1:ny); N=zeros(ne,ny);
-bigR =[G*Q_e*G' G*N;N'*G' R];
-[W,Wt]=fullrf(bigR);B1=W(1:size(G,1),:);
-D21=W(($+1-size(C,1)):$,:);
-C2=C;
-P21=syslin('c',A,B1,C2,D21);
-[K,X]=lqe(P21);
-//Riccati check:
-S=G*N;Q=B1*B1';
-(A-S*inv(R)*C2)*X+X*(A-S*inv(R)*C2)'-X*C2'*inv(R)*C2*X+Q-S*inv(R)*S'
-
-//Stability check:
-spec(A+K*C)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqr">lqr</link>
-            </member>
-            <member>
-                <link linkend="observer">observer</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg.xml
deleted file mode 100644 (file)
index 70d4976..0000000
+++ /dev/null
@@ -1,132 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - F Delebecque
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lqg">
-    <refnamediv>
-        <refname>lqg</refname>
-        <refpurpose>LQG compensator</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[K]=lqg(P,r)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list (augmented plant) in state-space form
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 row vector = (number of measurements, number of inputs)  (dimension of  the 2,2 part of <literal>P</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list (controller)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>lqg</literal>  computes the linear optimal LQG (H2) controller for the
-            "augmented" plant <literal>P=syslin('c',A,B,C,D)</literal> (continuous time) or
-            <literal>P=syslin('d',A,B,C,D)</literal> (discrete time).
-        </para>
-        <para>
-            The function <literal>lqg2stan</literal> returns <literal>P</literal> and <literal>r</literal> given the
-            nominal plant, weighting terms and variances of noises.
-        </para>
-        <para>
-            <literal>K</literal> is given by the following ABCD matrices:
-            <literal>[A+B*Kc+Kf*C+Kf*D*Kc,-Kf,Kc,0]</literal> where <literal>Kc=lqr(P12)</literal>
-            is the controller gain and <literal>Kf=lqe(P21)</literal> is the filter gain.
-            See example in <literal>lqg2stan</literal>.
-        </para>
-    </refsection>
-
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-  s=poly(0,'s');
-  Plant=syslin('c',[1/(s+1)*s/(s-1)^2]);     //Nominal Plant
-  P22=tf2ss(Plant);    //...in state-space form
-  [ny,nu,nx]=size(P22);
-  rand('seed',0);rand('normal');
-  bigQ=rand(nx+nu,nx+nu);
-  bigQ=bigQ*bigQ';
-  bigR=rand(nx+ny,nx+ny);
-  bigR=bigR*bigR';  //random weighting matrices
-  [Plqg,r]=lqg2stan(P22,bigQ,bigR);     //LQG pb as a standard problem
-  Klqg=lqg(Plqg,r);          //Controller
-  spec(h_cl(Plqg,r,Klqg))    //Check internal stability
-  [Slqg,Rlqg,Tlqg]=sensi(P22,Klqg);  //Sensitivity functions
-  frq=logspace(-3,3);     //10^-3  to 10^3
-  y=svplot(Slqg);       //Computes singular values;
-  gainplot(frq,y)   //Plot sing. values
- ]]></programlisting>
-        <scilab:image>
-            s=poly(0,'s');
-            Plant=syslin('c',[1/(s+1)*s/(s-1)^2]);     //Nominal Plant
-            P22=tf2ss(Plant);    //...in state-space form
-            [ny,nu,nx]=size(P22);
-            rand('seed',0);rand('normal');
-            bigQ=rand(nx+nu,nx+nu);
-            bigQ=bigQ*bigQ';
-            bigR=rand(nx+ny,nx+ny);
-            bigR=bigR*bigR';  //random weighting matrices
-            [Plqg,r]=lqg2stan(P22,bigQ,bigR);     //LQG pb as a standard problem
-            Klqg=lqg(Plqg,r);          //Controller
-            spec(h_cl(Plqg,r,Klqg))    //Check internal stability
-            [Slqg,Rlqg,Tlqg]=sensi(P22,Klqg);  //Sensitivity functions
-            frq=logspace(-3,3);     //10^-3  to 10^3
-            y=svplot(Slqg);       //Computes singular values;
-            gainplot(frq,y)   //Plot sing. values
-        </scilab:image>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqg2stan">lqg2stan</link>
-            </member>
-            <member>
-                <link linkend="lqr">lqr</link>
-            </member>
-            <member>
-                <link linkend="lqe">lqe</link>
-            </member>
-            <member>
-                <link linkend="h_inf">h_inf</link>
-            </member>
-            <member>
-                <link linkend="obscont">obscont</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg2stan.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg2stan.xml
deleted file mode 100644 (file)
index adef50a..0000000
+++ /dev/null
@@ -1,183 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - F Delebecque
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lqg2stan">
-    <refnamediv>
-        <refname>lqg2stan</refname>
-        <refpurpose>LQG to standard problem</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[P_aug,r]=lqg2stan(P,Qxu,Qwv)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P22</term>
-                <listitem>
-                    <para>
-                        State space representation of the nominal plant (<literal>nu</literal> inputs, <literal>ny</literal> outputs, <literal>nx</literal> states).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Qxu</term>
-                <listitem>
-                    <para>
-                        <literal>[Q,S;S',N]</literal> symmetric <literal>nx+nu</literal> by <literal>nx+nu</literal> weighting matrix.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Qwv</term>
-                <listitem>
-                    <para>
-                        <literal>[R,T;T',V]</literal> symmetric <literal>nx+ny</literal> by <literal>nx+ny</literal> covariance matrix.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        Row vector <literal>[ny nu]</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>P_aug</term>
-                <listitem>
-                    <para>
-                        Augmented plant state space representation (see: <link linkend="syslin">syslin</link>)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>lqg2stan</literal> returns the augmented plant for linear LQG (H2) controller
-            design problem defined by:
-        </para>
-        <itemizedlist>
-            <listitem>
-                <para>
-                    The nominal plant <literal>P22</literal>:described by
-                </para>
-                <latex style="display"
-                   align="left">\left\{\begin{array}{l}\dot{x}=A x+B
-                    u +w \\y=C x+D u +v\end{array}\right. \text{ for continuous time or }
-                    \left\{\begin{array}{l}x^+=A x+B u+w\\y=C
-                    x+D u +v\end{array}\right. \text{ for discrete time.}
-                </latex>
-            </listitem>
-            <listitem>
-                <para>
-                    The (instantaneous) cost function
-                    <latex><![CDATA[\left[\begin{array}{ll} x'&
-              u'\end{array}\right] Q_{xu}\left[\begin{array}{l} x\\
-              u\end{array}\right]]]></latex>.
-            </para>
-          </listitem>
-          <listitem>
-            <para>
-              The noises covariance matrix
-              <latex><![CDATA[\mathbb{E}(\left[\begin{array}{l}w\\v\end{array}\right]
-              \left[\begin{array}{ll}w'&v'\end{array}\right])=Q_{wv}
-              ]]></latex>
-                </para>
-            </listitem>
-        </itemizedlist>
-
-        <latex style="display"
-        align="left">\text{P_aug }=\left\{\begin{array}{l}\dot{x}=A x+B_1 W+B
-            u  \\y_1=C_1 x+D_{12}W\\y_2=-C x+D_{21} W+D u
-            \end{array}\right. \text{ for continuous time or }
-            \left\{\begin{array}{l}x^+=A x+B_1 W+B
-            u  \\y_1=C_1 x+D_{12} W \\y_2=-C x+D_{21} W+D u
-            \end{array}\right. \text{ for discrete time.}
-        </latex>
-
-        <caution>
-            <para>
-                Up to Scilab-5.5.2 lqg2stan returns wrong inverted values
-                (see <ulink url="http://bugzilla.scilab.org/show_bug.cgi?id=13751"> bug 13751</ulink>)
-                to obtain the good result one had to use <code>[P,r]=lqg2stan(-P,Qxu,Qwv)</code>.
-            </para>
-            <para>
-                This bug is fixed since Scilab-6.0.0, old codes must be modified accordingly.
-            </para>
-        </caution>
-    </refsection>
-    <refsection>
-        <title>Algorithm</title>
-        <para>
-            If <literal>[B1;D21]</literal> is a factor of
-            <literal>Qxu</literal>, <literal>[C1,D12]</literal> is a
-            factor of <literal>Qwv</literal> (see: <link
-            linkend="fullrf">fullrf</link>) then
-            <code>P_aug=syslin(P.dt,P.A,[B1,P.B],[C1;-P.C],[0,D12;D21,P.D])</code>
-        </para>
-
-    </refsection>
-
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-ny=2;nu=3;nx=4;
-P22=ssrand(ny,nu,nx);
-Qxu=rand(nx+nu,nx+nu);Qxu=Qxu*Qxu';
-Qwv=rand(nx+ny,nx+ny);Qwv=Qwv*Qwv';
-[P_aug,r]=lqg2stan(P,Qxu,Qwv);
-K=lqg(P_aug,r);  //K=LQG-controller
-spec(h_cl(P_aug,r,K))      //Closed loop should be stable
-//Same as Cl=P22/.K; spec(Cl('A'))
-
-s=poly(0,'s')
-lqg2stan(1/(s+2),eye(2,2),eye(2,2))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqg">lqg</link>
-            </member>
-            <member>
-                <link linkend="lqr">lqr</link>
-            </member>
-            <member>
-                <link linkend="lqe">lqe</link>
-            </member>
-            <member>
-                <link linkend="obscont">obscont</link>
-            </member>
-            <member>
-                <link linkend="h_inf">h_inf</link>
-            </member>
-            <member>
-                <link linkend="augment">augment</link>
-            </member>
-            <member>
-                <link linkend="fstabst">fstabst</link>
-            </member>
-            <member>
-                <link linkend="feedback">feedback</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg_ltr.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqg_ltr.xml
deleted file mode 100644 (file)
index 1155b48..0000000
+++ /dev/null
@@ -1,98 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lqg_ltr">
-    <refnamediv>
-        <refname>lqg_ltr</refname>
-        <refpurpose>LQG with loop transform recovery</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[kf,kc]=lqg_ltr(sl,mu,ro)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>sl</term>
-                <listitem>
-                    <para>
-                        linear system in state-space form (<literal>syslin</literal> list)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>mu,ro</term>
-                <listitem>
-                    <para> real positive numbers chosen ``small enough''</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>kf,kc</term>
-                <listitem>
-                    <para>controller and observer Kalman gains.</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            returns the Kalman gains for:
-        </para>
-        <programlisting role=""><![CDATA[
-         x = a*x + b*u + l*w1
-(sl)
-         y = c*x + mu*I*w2
-
-         z = h*x
- ]]></programlisting>
-        <para>
-            Cost function:
-        </para>
-        <programlisting role=""><![CDATA[
-         /+oo
-         |
-J    = E(| [z(t)'*z(t) + ro^2*u(t)'*u(t)]dt)
- lqg     |
-         / 0
-  ]]></programlisting>
-        <para>
-            The lqg/ltr approach looks for <literal>L,mu,H,ro</literal> such that:
-            J(lqg) = J(freq) where
-        </para>
-        <programlisting role=""><![CDATA[
-        /+oo        *  *           *
-J    =  | tr[S  W  W  S ] + tr[T  T]dw
- freq   |
-        /0
- ]]></programlisting>
-        <para>
-            and
-        </para>
-        <programlisting role=""><![CDATA[
- S = (I + G*K)^(-1)
- T = G*K*(I+G*K)^(-1)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="syslin">syslin</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqr.xml b/scilab/modules/cacsd/help/fr_FR/control_design/linear_quadratic/lqr.xml
deleted file mode 100644 (file)
index 8afd5ff..0000000
+++ /dev/null
@@ -1,143 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lqr">
-    <refnamediv>
-        <refname>lqr</refname>
-        <refpurpose>LQ compensator (full state)  </refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[K,X]=lqr(P12)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P12</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list (state-space linear system)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K,X</term>
-                <listitem>
-                    <para>two real matrices</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>lqr</literal>  computes the linear optimal LQ full-state gain
-            for the plant <literal>P12=[A,B2,C1,D12]</literal> in continuous or
-            discrete time.
-        </para>
-        <para>
-            <literal>P12</literal> is a <literal>syslin</literal> list (e.g. <literal>P12=syslin('c',A,B2,C1,D12)</literal>).
-        </para>
-        <para>
-            The cost function is l2-norm of <literal>z'*z</literal> with <literal>z=C1 x + D12 u</literal>
-            i.e. <literal>[x,u]' * BigQ * [x;u]</literal> where
-        </para>
-        <programlisting role=""><![CDATA[
-      [C1' ]               [Q  S]
-BigQ= [    ]  * [C1 D12] = [    ]
-      [D12']               [S' R]
- ]]></programlisting>
-        <para>
-            The gain <literal>K</literal> is such that <literal>A + B2*K</literal> is stable.
-        </para>
-        <para>
-            <literal>X</literal> is the stabilizing solution of the Riccati equation.
-        </para>
-        <para>
-            For a continuous plant:
-        </para>
-        <programlisting role=""><![CDATA[
-(A-B2*inv(R)*S')'*X+X*(A-B2*inv(R)*S')-X*B2*inv(R)*B2'*X+Q-S*inv(R)*S'=0
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-inv(R)*(B2'*X+S)
- ]]></programlisting>
-        <para>
-            For a discrete plant:
-        </para>
-        <programlisting role=""><![CDATA[
-X=A'*X*A-(A'*X*B2+C1'*D12)*pinv(B2'*X*B2+D12'*D12)*(B2'*X*A+D12'*C1)+C1'*C1;
- ]]></programlisting>
-        <programlisting role=""><![CDATA[
-K=-pinv(B2'*X*B2+D12'*D12)*(B2'*X*A+D12'*C1)
- ]]></programlisting>
-        <para>
-            An equivalent form for <literal>X</literal> is
-        </para>
-        <programlisting role=""><![CDATA[
-X=Abar'*inv(inv(X)+B2*inv(r)*B2')*Abar+Qbar
- ]]></programlisting>
-        <para>
-            with <literal>Abar=A-B2*inv(R)*S'</literal> and <literal>Qbar=Q-S*inv(R)*S'</literal>
-        </para>
-        <para>
-            The 3-blocks matrix pencils associated with these Riccati equations are:
-        </para>
-        <programlisting role=""><![CDATA[
-             discrete                           continuous
- |I   0    0|   | A    0    B2|         |I   0   0|   | A    0    B2|
-z|0   A'   0| - |-Q    I    -S|        s|0   I   0| - |-Q   -A'   -S|
- |0   B2'  0|   | S'   0     R|         |0   0   0|   | S'  -B2'   R|
- ]]></programlisting>
-        <para>
-            <warning>
-                Caution: It is assumed that matrix R is non singular. In particular,
-                the plant must be tall (number of outputs &gt;= number of inputs).
-            </warning>
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-A=rand(2,2);B=rand(2,1);   //two states, one input
-Q=diag([2,5]);R=2;     //Usual notations x'Qx + u'Ru
-Big=sysdiag(Q,R);    //Now we calculate C1 and D12
-[w,wp]=fullrf(Big);C1=wp(:,1:2);D12=wp(:,3:$);   //[C1,D12]'*[C1,D12]=Big
-P=syslin('c',A,B,C1,D12);    //The plant (continuous-time)
-[K,X]=lqr(P)
-spec(A+B*K)    //check stability
-norm(A'*X+X*A-X*B*inv(R)*B'*X+Q,1)  //Riccati check
-P=syslin('d',A,B,C1,D12);    // Discrete time plant
-[K,X]=lqr(P)
-spec(A+B*K)   //check stability
-norm(A'*X*A-(A'*X*B)*pinv(B'*X*B+R)*(B'*X*A)+Q-X,1) //Riccati check
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqe">lqe</link>
-            </member>
-            <member>
-                <link linkend="gcare">gcare</link>
-            </member>
-            <member>
-                <link linkend="leqr">leqr</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/kpure.xml b/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/kpure.xml
deleted file mode 100644 (file)
index f397648..0000000
+++ /dev/null
@@ -1,121 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"  xml:lang="fr" xml:id="kpure">
-    <refnamediv>
-        <refname>kpure</refname>
-        <refpurpose>continuous SISO system limit feedback gain</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>
-            K=kpure(sys [,tol])
-            [K,R]=kpure(sys [,tol])
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>sys</term>
-                <listitem>
-                    <para>SISO linear system (syslin)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>tol</term>
-                <listitem>
-                    <para>a positive scalar.  tolerance used to determine if a
-                        root is imaginary or not. The default value is
-                        <literal>1e-6</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K</term>
-                <listitem>
-                    <para>Real vector, the vector of gains for which at least
-                        one closed loop pole is imaginary.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>R</term>
-                <listitem>
-                    <para>Complex vector, the imaginary closed loop poles
-                        associated with the values of <literal>K</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>K=kpure(sys)</literal> computes the gains <literal>K</literal> such that the system
-            <literal>sys</literal> feedback by <literal>K(i)</literal> (<literal>sys/.K(i)</literal>) has  poles on imaginary axis.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-num=real(poly([-1+%i, -1-%i, -1+8*%i  -1-8*%i],'s'));
-den=real(poly([0.5 0.5  -6+7*%i  -6-7*%i  -3 -7 -11],'s'));
-h=num/den;
-
-[K,Y]=kpure(h)
-clf();evans(h)
-plot(real(Y),imag(Y),'+r')
- ]]></programlisting>
-        <scilab:image>
-            num=real(poly([-1+%i, -1-%i, -1+8*%i  -1-8*%i],'s'));
-            den=real(poly([0.5 0.5  -6+7*%i  -6-7*%i  -3 -7 -11],'s'));
-            h=num/den;
-
-            [K,Y]=kpure(h)
-            clf();evans(h)
-            plot(real(Y),imag(Y),'+r')
-        </scilab:image>
-        <programlisting role="example"><![CDATA[
-num=real(poly([-1+%i*1, -1-%i*1, 2+%i*8  2-%i*8 -2.5+%i*13 -2.5-%i*13],'s'));
-den=real(poly([1 1 3+%i*3 3-%i*3 -15+%i*7  -15-%i*7  -3 -7 -11],'s'));
-h=num/den;
-
-[K,Y]=kpure(h)
-clf();evans(h,100000)
-plot(real(Y),imag(Y),'+r')
- ]]></programlisting>
-        <scilab:image>
-            num=real(poly([-1+%i*1, -1-%i*1, 2+%i*8  2-%i*8 -2.5+%i*13 -2.5-%i*13],'s'));
-            den=real(poly([1 1 3+%i*3 3-%i*3 -15+%i*7  -15-%i*7  -3 -7 -11],'s'));
-            h=num/den;
-
-            [K,Y]=kpure(h)
-            clf();evans(h,100000)
-            plot(real(Y),imag(Y),'+r')
-        </scilab:image>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="evans">evans</link>
-            </member>
-            <member>
-                <link linkend="krac2">krac2</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/krac2.xml b/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/krac2.xml
deleted file mode 100644 (file)
index 93453c9..0000000
+++ /dev/null
@@ -1,70 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="krac2">
-    <refnamediv>
-        <refname>krac2</refname>
-        <refpurpose>continuous SISO system limit feedback gain</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>g=krac2(sys)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>sys</term>
-                <listitem>
-                    <para>SISO linear system (syslin)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>g</term>
-                <listitem>
-                    <para>constant</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>krac2(sys)</literal> computes the gains <literal>g</literal> such that the system
-            <literal>sys</literal> feedback by g (<literal>sys/.g</literal>) has  2 real equal poles.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-h=syslin('c',352*poly(-5,'s')/poly([0,0,2000,200,25,1],'s','c'));
-clf();evans(h,100)
-g=krac2(h)
-hf1=h/.g(1);roots(denom(hf1))
-hf2=h/.g(2);roots(denom(hf2))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="evans">evans</link>
-            </member>
-            <member>
-                <link linkend="kpure">kpure</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/ppol.xml b/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/ppol.xml
deleted file mode 100644 (file)
index 365df6c..0000000
+++ /dev/null
@@ -1,88 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="ppol">
-    <refnamediv>
-        <refname>ppol</refname>
-        <refpurpose>pole placement</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[K]=ppol(A,B,poles)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A,B</term>
-                <listitem>
-                    <para>
-                        real matrices of dimensions <literal>nxn</literal> and <literal>nxm</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>poles</term>
-                <listitem>
-                    <para>
-                        real or complex vector of dimension <literal>n</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K</term>
-                <listitem>
-                    <para>real matrix (negative feedback gain)</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>K=ppol(A,B,poles)</literal> returns a mxn gain matrix <literal>K</literal> such that
-            the eigenvalues of <literal>A-B*K</literal> are <literal>poles</literal>.
-            The pair <literal>(A,B)</literal> must be controllable. Complex number in <literal>poles</literal> must appear in conjugate pairs.
-        </para>
-        <para>
-            An output-injection gain <literal>F</literal> for <literal>(A,C)</literal> is obtained as follows:
-        </para>
-        <para>
-            <literal>Ft=ppol(A',C',poles);  F=Ft'</literal>
-        </para>
-        <para>
-            The algorithm is by P.H. Petkov.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-A=rand(3,3);B=rand(3,2);
-F=ppol(A,B,[-1,-2,-3]);
-spec(A-B*F)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="canon">canon</link>
-            </member>
-            <member>
-                <link linkend="stabil">stabil</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/stabil.xml b/scilab/modules/cacsd/help/fr_FR/control_design/pole_placement/stabil.xml
deleted file mode 100644 (file)
index 6771b0c..0000000
+++ /dev/null
@@ -1,131 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="stabil">
-    <refnamediv>
-        <refname>stabil</refname>
-        <refpurpose>stabilization</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>F=stabil(A,B,alfa)
-            K=stabil(Sys,alfa,beta)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>A</term>
-                <listitem>
-                    <para>
-                        square real matrix (<literal>nx x nx</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>B</term>
-                <listitem>
-                    <para>
-                        real matrix (<literal>nx x nu</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>alfa, beta</term>
-                <listitem>
-                    <para> real or complex vector (in conjugate pairs) or real number.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>F</term>
-                <listitem>
-                    <para>
-                        real matrix (<literal>nx x nu</literal>)
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Sys</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list) (<literal>m</literal> inputs, <literal>p</literal> outputs).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>p</literal> inputs, <literal>m</literal> outputs)
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            <literal>F=stabil(A,B,alfa)</literal> returns a gain matrix <literal>F</literal> such that
-            <literal>A+B*F</literal> is stable if pair <literal>(A,B)</literal> is stabilizable.
-            Assignable poles are set to <literal>alfa(1),alfa(2),...</literal>.
-            If <literal>(A,B)</literal> is not stabilizable a warning is given
-            and assignable poles are set to <literal>alfa(1),alfa(2),...</literal>.
-            If <literal>alfa</literal> is a number all eigenvalues are set to this
-            <literal>alfa</literal> (default value is <literal>alfa=-1</literal>).
-        </para>
-        <para>
-            <literal>K=stabil(Sys,alfa,beta)</literal> returns <literal>K</literal>, a compensator for <literal>Sys</literal>
-            such that <literal>(A,B)</literal>-controllable eigenvalues are set to
-            <literal>alfa</literal> and <literal>(C,A)</literal>-observable eigenvalues are set to <literal>beta</literal>.
-        </para>
-        <para>
-            All assignable closed loop poles (which are given by the
-            eigenvalues of <literal>Aclosed=h_cl(Sys,K)</literal> are set to <literal>alfa(i)</literal>'s
-            and <literal>beta(j)</literal>'s.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-// Gain:
-Sys=ssrand(0,2,5,list('st',2,3,3));
-A=Sys('A');B=Sys('B');F=stabil(A,B);
-spec(A) //2 controllable modes 2 unstable uncontrollable modes
-//and one stable uncontrollable mode
-spec(A+B*F) //the two controllable modes are set to -1.
-// Compensator:
-Sys=ssrand(3,2,5,list('st',2,3,3)); //3 outputs, 2 inputs, 5 states
-//2 controllables modes, 3 controllable or stabilizable modes.
-K=stabil(Sys,-2,-3);  //Compensator for Sys.
-spec(Sys('A'))
-spec(h_cl(Sys,K))   //K Stabilizes what can be stabilized.
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="st_ility">st_ility</link>
-            </member>
-            <member>
-                <link linkend="contr">contr</link>
-            </member>
-            <member>
-                <link linkend="ppol">ppol</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/fr_FR/control_design/tracking/gfrancis.xml b/scilab/modules/cacsd/help/fr_FR/control_design/tracking/gfrancis.xml
deleted file mode 100644 (file)
index 1ab7db7..0000000
+++ /dev/null
@@ -1,126 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="gfrancis">
-    <refnamediv>
-        <refname>gfrancis</refname>
-        <refpurpose>Francis equations for tracking</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[L,M,T]=gfrancis(Plant,Model)</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Plant</term>
-                <listitem>
-                    <para> a continuous time dynamical system in state-space representation.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Model</term>
-                <listitem>
-                    <para> a continuous time dynamical system in state-space representation.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>L,M,T</term>
-                <listitem>
-                    <para>real matrices</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Given the linear plant:
-        </para>
-        <programlisting role=""><![CDATA[
-x'= F*x + G*u
-y = H*x + J*u
- ]]></programlisting>
-        <para>
-            and the linear model
-        </para>
-        <programlisting role=""><![CDATA[
-xm'= A*xm + B*um
-ym = C*xm + D*um
- ]]></programlisting>
-        <para>
-            the goal is for the plant to track the model i.e. <literal>e = y - ym ---&gt; 0</literal>
-            while keeping stable the state x(t) of the plant.
-            <literal>u</literal> is given by feedforward and feedback
-        </para>
-        <programlisting role=""><![CDATA[
-u = L*xm + M*um + K*(x-T*xm) = [K , L-K*T] *(x,xm) + M*um
- ]]></programlisting>
-        <para>
-            The matrices T,L,M satisfy generalized Francis equations
-        </para>
-        <programlisting role=""><![CDATA[
-F*T + G*L = T*A
-H*T + J*L = C
-      G*M = T*B
-      J*M = D
- ]]></programlisting>
-        <para>
-            The matrix <literal>K</literal> must be chosen as stabilizing the pair <literal>(F,G)</literal>
-            See example of use in directory <literal>demos/tracking</literal>.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-Plant=ssrand(1,3,5);
-[F,G,H,J]=abcd(Plant);
-nw=4;nuu=2;A=rand(nw,nw);
-st=max(real(spec(A)));A=A-st*eye(A);
-B=rand(nw,nuu);C=2*rand(1,nw);D=0*rand(C*B);
-Model=syslin('c',A,B,C,D);
-[L,M,T]=gfrancis(Plant,Model);
-norm(F*T+G*L-T*A,1)
-norm(H*T+J*L-C,1)
-norm(G*M-T*B,1)
-norm(J*M-D,1)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lqg">lqg</link>
-            </member>
-            <member>
-                <link linkend="ppol">ppol</link>
-            </member>
-        </simplelist>
-    </refsection>
-    <refsection>
-        <title>History</title>
-        <revhistory>
-            <revision>
-                <revnumber>5.4.0</revnumber>
-                <revremark>
-                    <literal>Sl</literal> is now checked for
-                    continuous time linear dynamical system.  This modification
-                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
-                </revremark>
-            </revision>
-        </revhistory>
-    </refsection>
-</refentry>
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diff --git a/scilab/modules/cacsd/help/pt_BR/control_design/control_loop/augment.xml b/scilab/modules/cacsd/help/pt_BR/control_design/control_loop/augment.xml
deleted file mode 100644 (file)
index 11029e8..0000000
+++ /dev/null
@@ -1,161 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="pt" xml:id="augment">
-    <refnamediv>
-        <refname>augment</refname>
-        <refpurpose>augmented plant</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[P,r]=augment(G)
-            [P,r]=augment(G,flag1)
-            [P,r]=augment(G,flag1,flag2)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>G</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the nominal plant
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag1</term>
-                <listitem>
-                    <para>
-                        one of the following (upper case) character string: <literal> 'S' </literal>, <literal> 'R' </literal>, <literal> 'T' </literal> <literal> 'SR' </literal>, <literal> 'ST' </literal>, <literal> 'RT' </literal> <literal> 'SRT' </literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag2</term>
-                <listitem>
-                    <para>
-                        one of the following character string: <literal> 'o' </literal> (stands for 'output', this is the default value) or <literal>'i'</literal> (stands for 'input').
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the ``augmented'' plant
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 row vector, dimension of <literal>P22 = G</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            If <literal>flag1='SRT'</literal> (default value), returns the "full" augmented plant
-        </para>
-        <programlisting role=""><![CDATA[
-    [ I | -G]   -->'S'
-    [ 0 |  I]   -->'R'
-P = [ 0 |  G]   -->'T'
-    [-------]
-    [ I | -G]
- ]]></programlisting>
-        <para>
-            <literal> 'S' </literal>, <literal> 'R' </literal>, <literal> 'T' </literal> refer to the first three (block) rows
-            of <literal>P</literal> respectively.
-        </para>
-        <para>
-            If one of these letters is absent in <literal>flag1</literal>, the corresponding
-            row in <literal>P</literal> is missing.
-        </para>
-        <para>
-            If <literal>G</literal> is given in state-space form, the returned <literal>P</literal> is minimal.
-            <literal>P</literal> is calculated by: <literal>[I,0,0;0,I,0;-I,0,I;I,0,0]*[I,-G;0,I;I,0]</literal>.
-        </para>
-        <para>
-            The augmented plant associated with input sensitivity functions, namely
-        </para>
-        <programlisting role=""><![CDATA[
-    [ I | -I]   -->'S'  (input sensitivity)
-    [ G | -G]   -->'R'  (G*input sensitivity)
-P = [ 0 |  I]   -->'T'  (K*G*input sensitivity)
-    [-------]
-    [ G | -G]
-    ]]></programlisting>
-        <para>
-            is obtained by the command <literal>[P,r]=augment(G,flag,'i')</literal>. For
-            state-space <literal>G</literal>, this <literal>P</literal>
-            is calculated by: <literal>[I,-I;0,0;0,I;0,0]+[0;I;0;I]*G*[I,-I]</literal>
-            and is thus generically minimal.
-        </para>
-        <para>
-            Note that weighting functions can be introduced by left-multiplying
-            <literal>P</literal> by a diagonal system of appropriate dimension, e.g.,
-            <literal> P = sysdiag(W1,W2,W3,eye(G))*P</literal>.
-        </para>
-        <para>
-            Sensitivity functions can be calculated by <literal>lft</literal>. One has:
-        </para>
-        <para>
-            For output sensitivity functions [P,r]=augment(P,'SRT'):
-            lft(P,r,K)=[inv(eye()+G*K);K*inv(eye()+G*K);G*K*inv(eye()+G*K)];
-        </para>
-        <para>
-            For input sensitivity functions [P,r]=augment(P,'SRT','i'):
-            lft(P,r,K)=[inv(eye()+K*G);G*inv(eye()+K*G);K*G*inv(eye()+G*K)];
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-G=ssrand(2,3,2); //Plant
-K=ssrand(3,2,2); //Compensator
-[P,r]=augment(G,'T');
-T=lft(P,r,K);   //Complementary sensitivity function
-Ktf=ss2tf(K);Gtf=ss2tf(G);
-Ttf=ss2tf(T);T11=Ttf(1,1);
-Oloop=Gtf*Ktf;
-Tn=Oloop*inv(eye(Oloop)+Oloop);
-clean(T11-Tn(1,1));
-//
-[Pi,r]=augment(G,'T','i');
-T1=lft(Pi,r,K);T1tf=ss2tf(T1); //Input Complementary sensitivity function
-Oloop=Ktf*Gtf;
-T1n=Oloop*inv(eye(Oloop)+Oloop);
-clean(T1tf(1,1)-T1n(1,1))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lft">lft</link>
-            </member>
-            <member>
-                <link linkend="sensi">sensi</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/pt_BR/control_design/control_loop/feedback.xml b/scilab/modules/cacsd/help/pt_BR/control_design/control_loop/feedback.xml
deleted file mode 100644 (file)
index 1f350c7..0000000
+++ /dev/null
@@ -1,97 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="pt" xml:id="feedback">
-    <refnamediv>
-        <refname>feedback</refname>
-        <refpurpose>feedback operation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>Sl=Sl1/.Sl2</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sl1,Sl2</term>
-                <listitem>
-                    <para>
-                        linear systems (<literal>syslin</literal> list) in state-space or transfer form, or ordinary gain matrices.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Sl</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list) in state-space or transfer form
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            The feedback operation is denoted by <literal> /. </literal> (slashdot).
-            This command returns <literal>Sl=Sl1*(I+Sl2*Sl1)^-1</literal>, i.e the (negative)
-            feedback of <literal>Sl1</literal> and <literal>Sl2</literal>. <literal>Sl</literal> is the transfer
-            <literal> v -&gt; y</literal> for <literal> y = Sl1 u</literal>, <literal>u = v - Sl2 y</literal>.
-        </para>
-        <para>
-            The result is the same as <literal>Sl=LFT([0,I;I,-Sl2],Sl1)</literal>.
-        </para>
-        <para>
-            <warning>
-                Caution: do not use with decimal point (e.g. <literal>1/.1</literal> is ambiguous!)
-            </warning>
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-S1=ssrand(2,2,3);S2=ssrand(2,2,2);
-W=S1/.S2;
-ss2tf(S1/.S2)
-//Same operation by LFT:
-ss2tf(lft([zeros(2,2),eye(2,2);eye(2,2),-S2],S1))
-//Other approach: with constant feedback
-BigS=sysdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
-Bigclosed=BigS/.F;
-W1=Bigclosed(1:2,1:2);   //W1=W (in state-space).
-ss2tf(W1)
-//Inverting
-ss2tf(S1*inv(eye()+S2*S1))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="lft">lft</link>
-            </member>
-            <member>
-                <link linkend="sysdiag">sysdiag</link>
-            </member>
-            <member>
-                <link linkend="augment">augment</link>
-            </member>
-            <member>
-                <link linkend="obscont">obscont</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/pt_BR/control_design/control_loop/lft.xml b/scilab/modules/cacsd/help/pt_BR/control_design/control_loop/lft.xml
deleted file mode 100644 (file)
index 7543cfb..0000000
+++ /dev/null
@@ -1,144 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="pt" xml:id="lft">
-    <refnamediv>
-        <refname>lft</refname>
-        <refpurpose>linear fractional transformation</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[P1]=lft(P,K)
-            [P1]=lft(P,r,K)
-            [P1,r1]=lft(P,r,Ps,rs)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the ``augmented'' plant, implicitly partitioned into four blocks (two input ports and two output ports).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>K</term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), the controller (possibly an ordinary gain).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        1x2 row vector, dimension of <literal>P22</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>Ps  </term>
-                <listitem>
-                    <para>
-                        linear system (<literal>syslin</literal> list), implicitly partitioned into four blocks (two input ports and two output ports).
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>rs  </term>
-                <listitem>
-                    <para>
-                        1x2 row vector, dimension of <literal>Ps22</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Linear fractional transform between two standard plants
-            <literal>P</literal> and <literal>Ps</literal> in state space form or in
-            transfer form (<literal>syslin</literal> lists).
-        </para>
-        <para>
-            <literal>r= size(P22) rs=size(P22s)</literal>
-        </para>
-        <para>
-            <literal>lft(P,r, K)</literal> is the linear fractional transform
-            between <literal>P</literal> and a controller <literal>K</literal>
-            (<literal>K</literal> may be a gain or a controller in state space form
-            or in transfer form);
-        </para>
-        <para>
-            <literal>lft(P,K)</literal> is <literal>lft(P,r,K)</literal> with
-            <literal>r</literal>=size of <literal>K</literal> transpose;
-        </para>
-        <para>
-            <literal>P1= P11+P12*K* (I-P22*K)^-1 *P21</literal>
-        </para>
-        <para>
-            <literal>[P1,r1]=lft(P,r,Ps,rs)</literal> returns the generalized (2
-            ports) lft of <literal>P</literal> and <literal>Ps</literal>.
-        </para>
-        <para>
-            <literal>P1</literal> is the pair two-port interconnected plant and the
-            partition of <literal>P1</literal> into 4 blocks in given by
-            <literal>r1</literal> which is the dimension of the <literal>22</literal>
-            block of <literal>P1</literal>.
-        </para>
-        <para>
-            <literal>P</literal> and <literal>R</literal> can be PSSDs i.e. may admit a
-            polynomial <literal>D</literal> matrix.
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-s=poly(0,'s');
-P=[1/s, 1/(s+1); 1/(s+2),2/s]; K= 1/(s-1);
-lft(P,K)
-lft(P,[1,1],K)
-P(1,1)+P(1,2)*K*inv(1-P(2,2)*K)*P(2,1)   //Numerically dangerous!
-ss2tf(lft(tf2ss(P),tf2ss(K)))
-lft(P,-1)
-f=[0,0;0,1];w=P/.f; w(1,1)
-//Improper plant (PID control)
-W=[1,1;1,1/(s^2+0.1*s)];K=1+1/s+s
-lft(W,[1,1],K); ss2tf(lft(tf2ss(W),[1,1],tf2ss(K)))
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="sensi">sensi</link>
-            </member>
-            <member>
-                <link linkend="augment">augment</link>
-            </member>
-            <member>
-                <link linkend="feedback">feedback</link>
-            </member>
-            <member>
-                <link linkend="sysdiag">sysdiag</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/pt_BR/control_design/disturbance_decoupling/ddp.xml b/scilab/modules/cacsd/help/pt_BR/control_design/disturbance_decoupling/ddp.xml
deleted file mode 100644 (file)
index 3767a13..0000000
+++ /dev/null
@@ -1,175 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA -
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="pt" xml:id="ddp">
-    <refnamediv>
-        <refname>ddp</refname>
-        <refpurpose>disturbance decoupling</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[Closed,F,G]=ddp(Sys,zeroed,B1,D1)
-            [Closed,F,G]=ddp(Sys,zeroed,B1,D1,flag,alfa,beta)
-        </synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>Sys</term>
-                <listitem>
-                    <para>
-                        <literal>syslin</literal> list containing the matrices <literal>(A,B2,C,D2)</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>zeroed</term>
-                <listitem>
-                    <para>
-                        integer vector, indices of outputs of <literal>Sys</literal> which are zeroed.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>B1</term>
-                <listitem>
-                    <para>real matrix</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>D1</term>
-                <listitem>
-                    <para>
-                        real matrix. <literal>B1</literal> and <literal>D1</literal> have the same number of columns.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>flag</term>
-                <listitem>
-                    <para>
-                        string <literal>'ge'</literal> or <literal>'st'</literal> (default) or <literal>'pp'</literal>.
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>alpha</term>
-                <listitem>
-                    <para>real or complex vector (loc. of closed loop poles)</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>beta</term>
-                <listitem>
-                    <para>real or complex vector (loc. of closed loop poles)</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            Exact disturbance decoupling (output nulling algorithm).
-            Given a linear system, and a subset of outputs, z, which are to
-            be zeroed, characterize the inputs w of Sys such that the
-            transfer function from w to z is zero.
-            <literal>Sys</literal> is a linear system {A,B2,C,D2} with one input and two outputs
-            ( i.e.  Sys: u--&gt;(z,y) ), part the following system defined from <literal>Sys</literal>
-            and <literal>B1,D1</literal>:
-        </para>
-        <programlisting role=""><![CDATA[
-xdot =  A x + B1  w + B2  u
-   z = C1 x + D11 w + D12 u
-   y = C2 x + D21 w + D22 u
- ]]></programlisting>
-        <para>
-            outputs of Sys are partitioned into (z,y) where z is to be zeroed,
-            i.e. the matrices C and D2 are:
-        </para>
-        <programlisting role=""><![CDATA[
-C=[C1;C2]         D2=[D12;D22]
-C1=C(zeroed,:)    D12=D2(zeroed,:)
- ]]></programlisting>
-        <para>
-            The matrix <literal>D1</literal> is partitioned similarly as <literal>D1=[D11;D21]</literal>
-            with <literal>D11=D1(zeroed,:)</literal>.
-            The control is u=Fx+Gw and one  looks for matriced <literal>F,G</literal> such that the
-            closed loop system: w--&gt;z given by
-        </para>
-        <programlisting role=""><![CDATA[
-xdot= (A+B2*F)  x + (B1 + B2*G) w
-  z = (C1+D12F) x + (D11+D12*G) w
- ]]></programlisting>
-        <para>
-            has zero transfer transfer function.
-        </para>
-        <para>
-            <literal>flag='ge'</literal>no stability constraints.
-            <literal>flag='st'</literal> : look for stable closed loop system (A+B2*F stable).
-            <literal>flag='pp'</literal> : eigenvalues of A+B2*F are assigned to <literal>alfa</literal> and
-            <literal>beta</literal>.
-        </para>
-        <para>
-            Closed is a realization of the <literal>w--&gt;y</literal> closed loop system
-        </para>
-        <programlisting role=""><![CDATA[
-xdot= (A+B2*F)  x + (B1 + B2*G) w
-  y = (C2+D22*F) x + (D21+D22*G) w
- ]]></programlisting>
-        <para>
-            Stability (resp. pole placement) requires stabilizability
-            (resp. controllability) of (A,B2).
-        </para>
-    </refsection>
-    <refsection>
-        <title>Examples</title>
-        <programlisting role="example"><![CDATA[
-rand('seed',0);nx=6;nz=3;nu=2;ny=1;
-A=diag(1:6);A(2,2)=-7;A(5,5)=-9;B2=[1,2;0,3;0,4;0,5;0,0;0,0];
-C1=[zeros(nz,nz),eye(nz,nz)];D12=[0,1;0,2;0,3];
-Sys12=syslin('c',A,B2,C1,D12);
-C=[C1;rand(ny,nx)];D2=[D12;rand(ny,size(D12,2))];
-Sys=syslin('c',A,B2,C,D2);
-[A,B2,C1,D12]=abcd(Sys12);  //The matrices of Sys12.
-my_alpha=-1;my_beta=-2;flag='ge';
-[X,dims,F,U,k,Z]=abinv(Sys12,my_alpha,my_beta,flag);
-clean(X'*(A+B2*F)*X)
-clean(X'*B2*U)
-clean((C1+D12*F)*X)
-clean(D12*U);
-//Calculating an ad-hoc B1,D1
-G1=rand(size(B2,2),3);
-B1=-B2*G1;
-D11=-D12*G1;
-D1=[D11;rand(ny,size(B1,2))];
-
-[Closed,F,G]=ddp(Sys,1:nz,B1,D1,'st',my_alpha,my_beta);
-closed=syslin('c',A+B2*F,B1+B2*G,C1+D12*F,D11+D12*G);
-ss2tf(closed)
- ]]></programlisting>
-    </refsection>
-    <refsection role="see also">
-        <title>See also</title>
-        <simplelist type="inline">
-            <member>
-                <link linkend="abinv">abinv</link>
-            </member>
-            <member>
-                <link linkend="ui_observer">ui_observer</link>
-            </member>
-        </simplelist>
-    </refsection>
-</refentry>
diff --git a/scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/ccontrg.xml b/scilab/modules/cacsd/help/pt_BR/control_design/h_infinity/ccontrg.xml
deleted file mode 100644 (file)
index e78e406..0000000
+++ /dev/null
@@ -1,101 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!--
- * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
- * Copyright (C) INRIA - P. Gahinet
- *
- * Copyright (C) 2012 - 2016 - Scilab Enterprises
- *
- * This file is hereby licensed under the terms of the GNU GPL v2.0,
- * pursuant to article 5.3.4 of the CeCILL v.2.1.
- * This file was originally licensed under the terms of the CeCILL v2.1,
- * and continues to be available under such terms.
- * For more information, see the COPYING file which you should have received
- * along with this program.
- *
- -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="pt" xml:id="ccontrg">
-    <refnamediv>
-        <refname>ccontrg</refname>
-        <refpurpose>Central H-infinity continuous time controller</refpurpose>
-    </refnamediv>
-    <refsynopsisdiv>
-        <title>Syntax</title>
-        <synopsis>[K]=ccontrg(P,r,gamma);</synopsis>
-    </refsynopsisdiv>
-    <refsection>
-        <title>Arguments</title>
-        <variablelist>
-            <varlistentry>
-                <term>P</term>
-                <listitem>
-                    <para> a continuous time linear dynamical system in state-space representation.</para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>r</term>
-                <listitem>
-                    <para>
-                        a two elements vector with integer values: the dimension of the 2,2 part of <literal>P</literal>
-                    </para>
-                </listitem>
-            </varlistentry>
-            <varlistentry>
-                <term>gamma</term>
-                <listitem>
-                    <para>real number</para>
-                </listitem>
-            </varlistentry>
-        </variablelist>
-    </refsection>
-    <refsection>
-        <title>Description</title>
-        <para>
-            returns a realization <literal>K</literal> of the central controller for the
-            general standard problem in state-space form.
-        </para>
-        <para>
-            <note>
-                Note that gamma must be &gt; gopt (output of <literal>gamitg</literal>)
-            </note>
-        </para>
-        <para>
-