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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) INRIA - F Delebecque
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
*
-->
<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="sysfact">
<refnamediv>
<refname>sysfact</refname>
<refpurpose>system factorization</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[S,Series]=sysfact(Sys,Gain,flag)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>Sys</term>
<listitem>
<para>
<literal>syslin</literal> list containing the matrices <literal>[A,B,C,D]</literal>.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Gain</term>
<listitem>
<para>real matrix</para>
</listitem>
</varlistentry>
<varlistentry>
<term>flag</term>
<listitem>
<para>
string <literal>'post'</literal> or <literal>'pre'</literal>
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>S</term>
<listitem>
<para>
<literal>syslin</literal> list
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Series</term>
<listitem>
<para>
<literal>syslin</literal> list
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
If <literal>flag</literal> equals <literal>'post'</literal>, <literal>sysfact</literal> returns in <literal>S</literal> the linear
system with ABCD matrices <literal>(A+B*Gain, B , Gain, I)</literal>, and <literal>Series</literal>,
a minimal realization of the series system <literal>Sys*S</literal>.
If <literal>flag</literal> equals <literal>'pre'</literal>, <literal>sysfact</literal> returns the linear system
<literal>(A+Gain*C, Gain , C, I)</literal> and <literal>Series</literal>, a minimal realization of the
series system <literal>S*Sys</literal>.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Kalman filter
Sys=ssrand(3,2,4);Sys('D')=rand(3,2);
S=sysfact(Sys,lqr(Sys),'post');
ww=minss(Sys*S);
ss2tf(gtild(ww)*ww),Sys('D')'*Sys('D')
//Kernel
Sys=ssrand(2,3,4);
[X,d,F,U,k,Z]=abinv(Sys);
ss2tf(Sys*Z)
ss2tf(Sys*sysfact(Sys,F,'post')*U)
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="lqr">lqr</link>
</member>
<member>
<link linkend="lqe">lqe</link>
</member>
</simplelist>
</refsection>
</refentry>
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