<?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="lin">
    <refnamediv>
        <refname>lin</refname>
        <refpurpose>線形化</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>[A,B,C,D]=lin(sim,x0,u0)
            [sl]=lin(sim,x0,u0)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>パラメータ</title>
        <variablelist>
            <varlistentry>
                <term>sim</term>
                <listitem>
                    <para>関数</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>x0, u0</term>
                <listitem>
                    <para>互換性がある次元のベクトル</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>A,B,C,D</term>
                <listitem>
                    <para>実数行列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>sl</term>
                <listitem>
                    <para>
                        <literal>syslin</literal> リスト
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            非線形システム <literal>[y,xdot]=sim(x,u)</literal>の
            <literal>x0,u0</literal>近傍での線形化.
        </para>
        <para>
            <literal>sim</literal> は <literal>y</literal> および
            <literal>xdot</literal>を計算する関数です.
        </para>
        <para>
            出力は線形システム (<literal>syslin</literal> リスト) <literal>sl</literal> または
            4つの行列 <literal>(A,B,C,D)</literal>です.
        </para>
        <para>
            例えば,  <literal>ftz</literal> が ODE に指定された関数で,
            例えば以下の場合:
        </para>
        <programlisting role=""><![CDATA[
[zd]=ftz(t,z,u)
 ]]></programlisting>
        <para>
            そして,  <literal>y=x</literal>と仮定すると,
        </para>
        <para>
            <literal>[z]=ode(x0,t0,tf,list(ftz,u)</literal> は
            <literal>x(tf)</literal>を計算します.
        </para>
        <para>
            <literal>simula</literal> が以下の関数の場合:
        </para>
        <programlisting role=""><![CDATA[
deff('[y,xd]=simula(x,u)','xd=ftz(tf,x,u); y=x;');
 ]]></programlisting>
        <para>
            接する線形システム <literal>sl</literal> は以下のように得られます:
        </para>
        <programlisting role=""><![CDATA[
[A,B,C,D]=lin(simula,z,u)
sl = syslin('c',A,B,C,D,x0)
 ]]></programlisting>
    </refsection>
    <refsection>
        <title>例</title>
        <programlisting role="example"><![CDATA[
deff('[y,xdot]=sim(x,u)','xdot=[u*sin(x);-u*x^2];y=xdot(1)+xdot(2)')
sl=lin(sim,1,2);
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="external">external</link>
            </member>
            <member>
                <link linkend="derivat">derivat</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
