<?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="gcare">
    <refnamediv>
        <refname>gcare</refname>
        <refpurpose>制御リカッチ方程式</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>[X,F]=gcare(Sl)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>引数</title>
        <variablelist>
            <varlistentry>
                <term>Sl</term>
                <listitem>
                    <para>
                        状態空間表現の連続時間線形動的システム
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>対称行列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>F</term>
                <listitem>
                    <para>実数行列</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            一般化制御代数リカッチ方程式(GCARE).
            <literal>X</literal> = 解 , <literal>F</literal> = ゲイン.
        </para>
        <para>
            <literal>Sl=[A,B,C,D]</literal> に関するGCAREは次のようになります:
        </para>
        <programlisting role=""><![CDATA[
(A-B*Si*D'*C)'*X+X*(A-B*Si*D'*C)-X*B*Si*B'*X+C'*Ri*C=0
 ]]></programlisting>
        <para>
            ただし, <literal>S=(eye()+D'*D)</literal>, <literal>Si=inv(S)</literal>, <literal>R=(eye()+D*D')</literal>, <literal>Ri=inv(R)</literal>
            そして, <literal>F=-Si*(D'*C+B'*X)</literal> は<literal>A+B*F</literal>
            が安定となるように設定されます.
        </para>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="gfare">gfare</link>
            </member>
        </simplelist>
    </refsection>
    <refsection>
        <title>履歴</title>
        <revhistory>
            <revision>
                <revnumber>5.4.0</revnumber>
                <revremark>
                    <literal>Sl</literal> は連続時間線形動的システム
                    について確認されるようになりました.
                    この修正はこの
                    <ulink url="https://gitlab.com/scilab/scilab/-/commit/3d7083daae3339813ba747c8adcda1f9599bb80d">コミット</ulink>により導入されました.
                </revremark>
            </revision>
        </revhistory>
    </refsection>
</refentry>
