<?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:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lyap" xml:lang="pt">
    <refnamediv>
        <refname>lyap</refname>
        <refpurpose>equação de Lyapunov</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Seqüência de Chamamento</title>
        <synopsis>[X]=lyap(A,C,'c')
            [X]=lyap(A,C,'d')
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Parâmetros</title>
        <variablelist>
            <varlistentry>
                <term>A, C</term>
                <listitem>
                    <para>
                        matrizes quadradas de reais, <literal>C</literal> deve ser
                        simétrica
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Descrição</title>
        <para>
            <literal>X= lyap(A,C,flag)</literal> resolve as equações matriciais
            de tempo contínuo ou de tempo discreto de Lyapunov:
        </para>
        <programlisting role=""><![CDATA[
A'*X + X*A = C       ( flag='c' )
A'*X*A - X = C       ( flag='d' )
 ]]></programlisting>
        <para>Perceba que existe uma única solução se e só se um autovalor de
            <literal>A</literal> não é um autovalor de <literal>-A</literal>
            (<literal>flag='c'</literal>) ou 1 sobre um autovalor de
            <literal>A</literal> (<literal>flag='d'</literal>).
        </para>
    </refsection>
    <refsection>
        <title>Exemplos</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>Ver Também</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>
