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>