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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 - Serge STEER
*
* 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="minreal">
<refnamediv>
<refname>minreal</refname>
<refpurpose>minimal balanced realization</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>slb=minreal(sl [,tol])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>sl,slb</term>
<listitem>
<para>
<literal>syslin</literal> lists
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>tol</term>
<listitem>
<para>real (threshold)</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>[ae,be,ce]=minreal(a,b,c,domain [,tol]) </literal>
returns the balanced realization of linear
system <literal>sl</literal> (<literal>syslin</literal> list).
</para>
<para>
<literal>sl</literal> is assumed stable.
</para>
<para>
<literal>tol</literal> threshold used in <literal>equil1</literal>.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
A=[-eye(2,2),rand(2,2);zeros(2,2),-2*eye(2,2)];
B=[rand(2,2);zeros(2,2)];C=rand(2,4);
sl=syslin('c',A,B,C);
slb=minreal(sl);
ss2tf(sl)
ss2tf(slb)
ctr_gram(sl)
clean(ctr_gram(slb))
clean(obs_gram(slb))
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="minss">minss</link>
</member>
<member>
<link linkend="balreal">balreal</link>
</member>
<member>
<link linkend="arhnk">arhnk</link>
</member>
<member>
<link linkend="equil">equil</link>
</member>
<member>
<link linkend="equil1">equil1</link>
</member>
</simplelist>
</refsection>
</refentry>
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