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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE
*
* 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-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" version="5.0-subset Scilab" xml:lang="en" xml:id="pol2des">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>pol2des</refname>
<refpurpose> polynomial matrix to descriptor form</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[N,B,C]=pol2des(Ds)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>Ds</term>
<listitem>
<para>polynomial matrix</para>
</listitem>
</varlistentry>
<varlistentry>
<term>N, B, C</term>
<listitem>
<para>three real matrices</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Given the polynomial matrix <literal>Ds=D_0 +D_1 s +D_2 s^2 +... +D_k s^k</literal>,
<literal>pol2des</literal> returns three matrices <literal>N, B, C</literal>, with <literal>N</literal> nilpotent
such that:</para>
<para>
<literal>Ds = C (s*N-eye())^-1 B</literal>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
s=poly(0,'s');
G=[1,s;1+s^2,3*s^3];[N,B,C]=pol2des(G);
G1=clean(C*inv(s*N-eye())*B),G2=numer(G1)
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="ss2des">ss2des</link>
</member>
<member>
<link linkend="tf2des">tf2des</link>
</member>
</simplelist>
</refsection>
<refsection>
<title>Authors</title>
<para>F.D.; </para>
</refsection>
</refentry>
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