<?xml version="1.0" encoding="UTF-8"?>
<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="fr" xml:id="pol2des">
    <refnamediv>
        <refname>pol2des</refname>
        <refpurpose>conversion matrice de polynômes vers forme descripteur  </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Séquence d'appel</title>
        <synopsis>[N,B,C]=pol2des(Ds)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Paramètres</title>
        <variablelist>
            <varlistentry>
                <term>Ds  </term>
                <listitem>
                    <para>matrice de polynômes
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>N, B, C  </term>
                <listitem>
                    <para>3 matrices réelles
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Etant donnée la matrice de polynômes <literal>Ds=D_0 +D_1 s +D_2 s^2 +... +D_k s^k</literal>,
            <literal>pol2des</literal> renvoie 3 matrices <literal>N, B, C</literal>, avec <literal>N</literal> nilpotente
            telles que :
        </para>
        <para>
            <literal>Ds = C (s*N-eye())^-1 B </literal>
        </para>
    </refsection>
    <refsection>
        <title>Exemples</title>
        <programlisting role="example"><![CDATA[
s = poly(0,'s');
G = [1, s; 1+s^2, 3*s^3];
[N, B, C] = pol2des(G);
G1 = clean(C*inv(s*N-eye())*B)
G2 = G1.num
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>Voir aussi</title>
        <simplelist type="inline">
            <member>
                <link linkend="ss2des">ss2des</link>
            </member>
            <member>
                <link linkend="tf2des">tf2des</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
