<?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="en" xml:id="sysfact">
    <refnamediv>
        <refname>sysfact</refname>
        <refpurpose>system factorization</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</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>
