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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="balreal">
<refnamediv>
<refname>balreal</refname>
<refpurpose>balanced realization</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[slb [,U] ] = balreal(sl)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>sl,slb</term>
<listitem>
<para>
linear systems (<literal>syslin</literal> lists)
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Balanced realization of linear system <literal>sl=[A,B,C,D]</literal>. <literal>sl</literal>
can be a continuous-time or discrete-time state-space system.
sl is assumed stable.
</para>
<programlisting role=""><![CDATA[
slb=[inv(U)*A*U ,inv(U)*B , C*U , D]
]]></programlisting>
<para>
is the balanced realization.
</para>
<para>
<literal>slb</literal> is returned as a <literal>syslin</literal> list.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
A=diag([-1,-2,-3,-4,-5]);B=rand(5,2);C=rand(1,5);
sl=syslin('c',A,B,C);
[slb,U]=balreal(sl);
Wc=clean(ctr_gram(slb))
W0=clean(obs_gram(slb))
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="ctr_gram">ctr_gram</link>
</member>
<member>
<link linkend="obs_gram">obs_gram</link>
</member>
<member>
<link linkend="hankelsv">hankelsv</link>
</member>
<member>
<link linkend="equil">equil</link>
</member>
<member>
<link linkend="equil1">equil1</link>
</member>
</simplelist>
</refsection>
</refentry>
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