5ce83ec8d07b43f5c8ab56ef3c01b26a60c7050c
[scilab.git] / scilab / modules / cacsd / help / en_US / linear_system_factorization / rowinout.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="rowinout">
17     <refnamediv>
18         <refname>rowinout</refname>
19         <refpurpose>inner-outer factorization</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Syntax</title>
23         <synopsis>[Inn,X,Gbar]=rowinout(G)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Arguments</title>
27         <variablelist>
28             <varlistentry>
29                 <term>G</term>
30                 <listitem>
31                     <para>
32                         linear system (<literal>syslin</literal> list) <literal>[A,B,C,D]</literal>
33                     </para>
34                 </listitem>
35             </varlistentry>
36             <varlistentry>
37                 <term>Inn</term>
38                 <listitem>
39                     <para>
40                         inner factor (<literal>syslin</literal> list)
41                     </para>
42                 </listitem>
43             </varlistentry>
44             <varlistentry>
45                 <term>Gbar</term>
46                 <listitem>
47                     <para>
48                         outer factor (<literal>syslin</literal> list)
49                     </para>
50                 </listitem>
51             </varlistentry>
52             <varlistentry>
53                 <term>X</term>
54                 <listitem>
55                     <para>
56                         row-compressor of <literal>G</literal> (<literal>syslin</literal> list)
57                     </para>
58                 </listitem>
59             </varlistentry>
60         </variablelist>
61     </refsection>
62     <refsection>
63         <title>Description</title>
64         <para>
65             Inner-outer factorization (and row compression) of (<literal>l</literal>x<literal>p</literal>) <literal>G =[A,B,C,D]</literal> with <literal>l&gt;=p</literal>.
66         </para>
67         <para>
68             <literal>G</literal> is assumed to be tall (<literal>l&gt;=p</literal>) without zero on the imaginary axis
69             and with a <literal>D</literal> matrix which is full column rank.
70         </para>
71         <para>
72             <literal>G</literal> must also be stable for having <literal>Gbar</literal> stable.
73         </para>
74         <para>
75             <literal>G</literal> admits the following inner-outer factorization:
76         </para>
77         <programlisting role=""><![CDATA[
78  G = [ Inn ] | Gbar |
79              |  0   |
80  ]]></programlisting>
81         <para>
82             where <literal>Inn</literal> is square and inner (all pass and stable) and <literal>Gbar</literal>
83             square and outer i.e:
84             Gbar is square bi-proper and bi-stable (Gbar inverse is also proper
85             and stable);
86         </para>
87         <para>
88             Note that:
89         </para>
90         <programlisting role=""><![CDATA[
91       [ Gbar ]
92 X*G = [  -   ]
93       [  0   ]
94  ]]></programlisting>
95         <para>
96             is a row compression of <literal>G</literal> where <literal>X</literal> = <literal>Inn</literal> inverse is all-pass i.e:
97         </para>
98         <programlisting role=""><![CDATA[
99  T
100 X (-s) X(s) = Identity
101  ]]></programlisting>
102         <para>
103             (for the continuous time case).
104         </para>
105     </refsection>
106     <refsection role="see also">
107         <title>See also</title>
108         <simplelist type="inline">
109             <member>
110                 <link linkend="syslin">syslin</link>
111             </member>
112             <member>
113                 <link linkend="colinout">colinout</link>
114             </member>
115         </simplelist>
116     </refsection>
117 </refentry>