<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( https://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) Scilab Enterprises - 2013 - Charlotte HECQUET
 * 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="fspec">
    <refnamediv>
        <refname>fspec</refname>
        <refpurpose>spectral factorization of continuous time dynamical systems</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>gm = fspec(g)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>g</term>
                <listitem>
                    <para> a continuous time linear dynamical system.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>gm</term>
                <listitem>
                    <para> a continuous time linear dynamical system.</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            returns <literal>gm</literal> with <literal>gm</literal> and <literal>gm^-1</literal> stable such that:
        </para>
        <programlisting role="no-scilab-exec"><![CDATA[
g = gtild(gm)*gm
 ]]></programlisting>
        <para>
            gtild(gm) returns a state-space representation of gm(-s)'.
        </para>

        <para>
            <literal>g</literal> is inversible.
        </para>
        <para>
            Imaginary-axis poles are forbidden.
        </para>
        <para>
            gtild(g)=g (poles and zeros of g are symmetric wrt imaginary axis).
        </para>
        <para>
            g(inf) is positive definite.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
a=-1000;
b=5;
c=5;
d=5;
sl=syslin('c',a,b,c,d);
fspec(sl)
 ]]></programlisting>
    </refsection>
</refentry>
