<?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="ja" xml:id="lyap">

    <refnamediv>

        <refname>lyap</refname>

        <refpurpose>リアプノフ方程式</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[X]=lyap(A,C,'c')

            [X]=lyap(A,C,'d')

        </synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A, C</term>

                <listitem>

                    <para>

                        実数正方行列, <literal>C</literal> は対称であることが必要

                    </para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            <literal>X= lyap(A,C,flag)</literal> は連続時間または離散時間行列

            リアプノフ方程式を解きます:

        </para>

        <programlisting role=""><![CDATA[
A'*X + X*A = C       ( flag='c' )
A'*X*A - X = C       ( flag='d' )
 ]]></programlisting>

        <para>

            <note>

                <literal>A</literal>の固有値が<literal>-A</literal>の

                固有値でない場合(<literal>flag='c'</literal>)

                または<literal>A</literal>の固有値分の1の場合

                (<literal>flag='d'</literal>)にのみユニークな

                解が得られることに注意してください.

            </note>

        </para>

    </refsection>

    <refsection>

        <title>例</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>参照</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>

