<?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="gfare">
    <refnamediv>
        <refname>gfare</refname>
        <refpurpose>フィルタリカッチ方程式</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>[Z,H]=gfare(Sl)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>パラメータ</title>
        <variablelist>
            <varlistentry>
                <term>Sl</term>
                <listitem>
                    <para>
                        線形システム (<literal>syslin</literal> リスト)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Z</term>
                <listitem>
                    <para>対称行列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>H</term>
                <listitem>
                    <para>実数行列</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            一般化フィルタ代数リカッチ方程式 (GFARE).
            <literal>Z</literal> = 解, <literal>H</literal> = ゲイン.
        </para>
        <para>
            <literal>Sl=[A,B,C,D]</literal> の GFARE は次のようになります:
        </para>
        <programlisting role=""><![CDATA[
(A-B*D'*Ri*C)*Z+Z*(A-B*D'*Ri*C)'-Z*C'*Ri*C*Z+B*Si*B'=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>H=-(B*D'+Z*C')*Ri</literal> は
            <literal>A+H*C</literal> が安定となるよう設定されます.
        </para>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="gcare">gcare</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
