<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( https://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) INRIA - Serge STEER
 * 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="minreal">
    <refnamediv>
        <refname>minreal</refname>
        <refpurpose>minimal balanced realization</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            slb = minreal(sl)
            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>
