<?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="ric_desc">
    <refnamediv>
        <refname>ric_desc</refname>
        <refpurpose>リカッチ方程式 <emphasis role="bold">(obsolete)</emphasis></refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>X=ric_desc(H [,E))
            [X1,X2,zero]=ric_desc(H [,E])
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>パラメータ</title>
        <variablelist>
            <varlistentry>
                <term>H,E</term>
                <listitem>
                    <para>実数正方行列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>X1,X2</term>
                <listitem>
                    <para>実数正方行列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>zero</term>
                <listitem>
                    <para>実数</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <warning>
            <para>
                This function is obsolete and will be removed from Scilab 6.1.x. Please use
                <literal>riccati(H)</literal> or <literal>riccati(H,E)</literal> instead.
            </para>
        </warning>
        <para>
            ハミルトン行列を入力とするリカッチソルバ.
        </para>
        <para>
            連続系の場合, 呼び出し手順は <literal>ric_descr(H)</literal> (1入力)となります:
        </para>
        <para>
            リカッチ方程式は次のようになります:
        </para>
        <programlisting role=""><![CDATA[
(Ec)   A'*X + X*A + X*R*X -Q = 0.
 ]]></programlisting>
        <para>
            ハミルトン行列 <literal>H</literal> は次のように定義できます:
        </para>
        <programlisting role=""><![CDATA[
H = [A  R;
     Q -A']
 ]]></programlisting>
        <para>
            呼び出し手順 <literal>[X1,X2,zero]=ric_descr(H)</literal>の場合,
            解は<literal>X=X1/X2</literal>で得られます.
        </para>
        <para>
            <literal>zero</literal> = (<literal>Ec</literal>)の右辺のL1ノルム
        </para>
        <para>
            解<literal>X</literal> は, <literal>X=riccati(A,Q,R,'c'))</literal>
            によっても得られます.
        </para>
        <para>
            離散時間の場合, 呼び出し手順は <literal>ric_descr(H,E)</literal> (2入力)となります:
        </para>
        <para>
            リカッチ解は以下のようになります:
        </para>
        <programlisting role=""><![CDATA[
(Ed)  A'*X*A-(A'*X*B*(R+B'*X*B)^-1)*(B'*X*A)+C-X = 0.
 ]]></programlisting>
        <para>
            <literal>G=B/R*B'</literal>と定義すると,
            ハミルトン行列のペンシル<literal>(E,H)</literal>は
            以下のようになります:
        </para>
        <programlisting role=""><![CDATA[
E=[eye(n,n),G;               H=[A, 0*ones(n,n);
   0*ones(n,n),A']             -C, eye(n,n)];
 ]]></programlisting>
        <para>
            呼び出し手順  <literal>[X1,X2,err]=ric_descr(H,E)</literal>の場合,
            <literal>X</literal>の解は<literal>X=X1/X2</literal>で得られます.
        </para>
        <para>
            <literal>zero</literal>= (<literal>Ed</literal>)の右辺のL1ノルム
        </para>
        <para>
            解 <literal>X</literal> <literal>X=riccati(A,G,C,'d')</literal>
            'ただし,<literal>G=B/R*B'</literal>) によっても得られます.
        </para>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="riccati">riccati</link>
            </member>
        </simplelist>
    </refsection>
    <refsection role="history">
        <title>履歴</title>
        <revhistory>
            <revision>
                <revnumber>6.1.0</revnumber>
                <revdescription>
                    <literal>ric_desc()</literal> is declared obsolete. <literal>riccati()</literal>
                    replaces it.
                </revdescription>
            </revision>
        </revhistory>
    </refsection>
</refentry>
