<?xml version="1.0" encoding="UTF-8"?>
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<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="lyap">
    <refnamediv>
        <refname>lyap </refname>
        <refpurpose>Equation de Lyapunov  </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Séquence d'appel</title>
        <synopsis>[X]=lyap(A,C,flag)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Paramètres</title>
        <variablelist>
            <varlistentry>
                <term>A, C  </term>
                <listitem>
                    <para>
                        matrices réelles, <literal>C</literal> doit être symétrique
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>flag  </term>
                <listitem>
                    <para>chaîne de caractères, 'c' ou 'd'
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>X= lyap(A,C,flag)</literal> résout l'équation matricielle de
            Lyapunov en temps continu ou discret
        </para>
        <programlisting role=""><![CDATA[
A'*X + X*A = C       ( flag = 'c' )
A'*X*A - X = C       ( flag = 'd' )
 ]]></programlisting>
        <para>
            Une solution unique existe si <literal>A</literal> n'a pas de valeur propre
            sur l'axe imaginaire (<literal>flag='c'</literal>) ou si 1 n'est pas
            valeur propre de <literal>A</literal> (<literal>flag='d'</literal>).
        </para>
    </refsection>
    <refsection>
        <title>Exemples</title>
        <programlisting role="example"><![CDATA[
A=rand(4,4);C=rand(A);C=C+C';
X=lyap(A,C,'c');
A'*X + X*A -C
X=lyap(A,C,'d');
A'*X*A - X -C
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>Voir aussi</title>
        <simplelist type="inline">
            <member>
                <link linkend="sylv">sylv</link>
            </member>
            <member>
                <link linkend="ctr_gram">ctr_gram</link>
            </member>
            <member>
                <link linkend="obs_gram">obs_gram</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
