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[scilab.git] / scilab / modules / cacsd / help / en_US / gcare.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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16 <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="gcare">
17     <refnamediv>
18         <refname>gcare</refname>
19         <refpurpose>Continuous time control Riccati equation</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Calling Sequence</title>
23         <synopsis>[X,F]=gcare(Sl)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Arguments</title>
27         <variablelist>
28             <varlistentry>
29                 <term>Sl</term>
30                 <listitem>
31                     <para>a continuous time linear dynamical system in state-space representation</para>
32                 </listitem>
33             </varlistentry>
34             <varlistentry>
35                 <term>X</term>
36                 <listitem>
37                     <para>symmetric matrix</para>
38                 </listitem>
39             </varlistentry>
40             <varlistentry>
41                 <term>F</term>
42                 <listitem>
43                     <para>real matrix</para>
44                 </listitem>
45             </varlistentry>
46         </variablelist>
47     </refsection>
48     <refsection>
49         <title>Description</title>
50         <para>
51             Generalized Control Algebraic Riccati Equation (GCARE).
52             <literal>X</literal> = solution , <literal>F</literal> = gain.
53         </para>
54         <para>
55             The GCARE for <literal>Sl=[A,B,C,D]</literal> is:
56         </para>
57         <programlisting role=""><![CDATA[ 
58 (A-B*Si*D'*C)'*X+X*(A-B*Si*D'*C)-X*B*Si*B'*X+C'*Ri*C=0
59  ]]></programlisting>
60         <para>
61             where <literal>S=(eye()+D'*D)</literal>, <literal>Si=inv(S)</literal>, <literal>R=(eye()+D*D')</literal>, <literal>Ri=inv(R)</literal> 
62             and <literal>F=-Si*(D'*C+B'*X)</literal> is such that <literal>A+B*F</literal> is stable.
63         </para>
64     </refsection>
65     <refsection role="see also">
66         <title>See Also</title>
67         <simplelist type="inline">
68             <member>
69                 <link linkend="gfare">gfare</link>
70             </member>
71         </simplelist>
72     </refsection>
73     <refsection>
74         <title>History</title>
75         <revhistory>
76             <revision>
77                 <revnumber>5.4.0</revnumber>
78                 <revremark>
79                     <literal>Sl</literal> is now checked for
80                     continuous time linear dynamical system.  This modification
81                     has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
82                 </revremark>
83             </revision>
84         </revhistory>
85     </refsection>
86 </refentry>