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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 -
*
* 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="copfac">
<refnamediv>
<refname>copfac</refname>
<refpurpose>right coprime factorization of continuous time dynamical systems</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[N,M,XT,YT]=copfac(G [,polf,polc,tol])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>G</term>
<listitem>
<para>a continuous-time linear dynamical system.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>polf, polc</term>
<listitem>
<para>
respectively the poles of <literal>XT</literal> and <literal>YT</literal> and the poles of <literal>n</literal> and <literal>M</literal> (default values =-1).
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>tol</term>
<listitem>
<para>
real threshold for detecting stable poles (default value <literal>100*%eps</literal>)
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>N,M,XT,YT</term>
<listitem>
<para>continuous-time linear dynamical systems.</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>[N,M,XT,YT]=copfac(G,[polf,polc,[tol]])</literal> returns a right coprime factorization of <literal>G</literal>.
</para>
<para>
<literal>G= N*M^-1</literal> where <literal>N</literal> and <literal>M</literal> are stable, proper and right coprime.
(i.e. <literal>[N M]</literal> left-invertible with stability)
</para>
<para>
<literal>XT</literal> and <literal>YT</literal> satisfy:
</para>
<para>
<literal>[XT -YT].[M N]' = eye</literal> (Bezout identity)
</para>
<para>
<literal>G</literal> is assumed stabilizable and detectable.
</para>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="syslin">syslin</link>
</member>
<member>
<link linkend="lcf">lcf</link>
</member>
</simplelist>
</refsection>
<refsection>
<title>History</title>
<revhistory>
<revision>
<revnumber>5.4.0</revnumber>
<revremark>
<literal>Sl</literal> is now checked for continuous time linear dynamical system.
This modification has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
</revremark>
</revision>
</revhistory>
</refsection>
</refentry>
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