<?xml version="1.0" encoding="UTF-8"?>
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 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
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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="st_ility">
    <refnamediv>
        <refname>st_ility</refname>
        <refpurpose>安定性テスト</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>[ns, [nc, [,U [,Slo] ]]]=st_ility(Sl [,tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>パラメータ</title>
        <variablelist>
            <varlistentry>
                <term>Sl</term>
                <listitem>
                    <para>
                        <literal>syslin</literal> リスト (線形システム)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>ns</term>
                <listitem>
                    <para> 整数 (可安定な部分空間の次元)</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>nc</term>
                <listitem>
                    <para>
                        整数 (可制御な部分空間の次元 <literal>nc &lt;= ns</literal>)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>U</term>
                <listitem>
                    <para>
                        最初の<literal>ns</literal>個(または <literal>nc</literal>個)の要素に
                        可安定(または可制御)な部分空間が広がる基底.
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Slo</term>
                <listitem>
                    <para>
                        線形システム (<literal>syslin</literal> リスト)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>可制御性検出の閾値 (contr参照)</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            <literal> Slo=( U'*A*U, U'*B, C*U, D, U'*x0 )</literal> (<literal>syslin</literal> リスト)
            は<literal>Sl</literal>の可安定形式を表示します.
            可安定とは<literal>ns=nx</literal> ( <literal>A</literal> 行列の次元)を意味します.
        </para>
        <programlisting role=""><![CDATA[
         [*,*,*]            [*]
U'*A*U = [0,*,*]     U'*B = [0]
         [0,0,*]            [0]
 ]]></programlisting>
        <para>
            ただし, <literal> (A11,B1) </literal> (dim(A11)= <literal>nc</literal>) は可制御で
            <literal>A22</literal>
            (dim(A22)=<literal>ns-nc</literal>) は安定です.
            "安定" は,
            (<literal>syslin</literal>の定義と同様,)
            連続線形システムの場合は固有値の実部が負,
            離散時間システムの場合は固有値の大きさが1未満であることを意味します.
        </para>
    </refsection>
    <refsection>
        <title>例</title>
        <programlisting role="example"><![CDATA[
A=diag([0.9,-2,3]);B=[0;0;1];Sl=syslin('c',A,B,[]);
[ns,nc,U]=st_ility(Sl);
U'*A*U
U'*B
[ns,nc,U]=st_ility(syslin('d',A,B,[]));
U'*A*U
U'*B
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="dt_ility">dt_ility</link>
            </member>
            <member>
                <link linkend="contr">contr</link>
            </member>
            <member>
                <link linkend="stabil">stabil</link>
            </member>
            <member>
                <link linkend="ssrand">ssrand</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
