1<?xml version="1.0" encoding="UTF-8"?>
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16<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="bilin">
17    <refnamediv>
18        <refname>bilin</refname>
19        <refpurpose>一般化双一次変換</refpurpose>
20    </refnamediv>
21    <refsynopsisdiv>
22        <title>呼び出し手順</title>
23        <synopsis>[sl1]=bilin(sl,v)</synopsis>
24    </refsynopsisdiv>
25    <refsection>
26        <title>パラメータ</title>
27        <variablelist>
28            <varlistentry>
29                <term>sl,sl1</term>
30                <listitem>
31                    <para>
32                        線形システム (<literal>syslin</literal> リスト)
33                    </para>
34                </listitem>
35            </varlistentry>
36            <varlistentry>
37                <term>v</term>
38                <listitem>
39                    <para>
40                        4つのエントリを有する実数ベクトル (<literal>v=[a,b,c,d]</literal>)
41                    </para>
42                </listitem>
43            </varlistentry>
44        </variablelist>
45    </refsection>
46    <refsection>
47        <title>説明</title>
48        <para>
49            線形システムを状態空間形式<literal>sl=syslin(dom,A,B,C,D)</literal>
50            (<literal>syslin</literal> リスト)
51            で指定すると,
52            <literal>sl1=bilin(sl,v)</literal> は行列<literal>[A1,B1,C1,D1]</literal>を有する
53            線形システム<literal>sl1</literal>を返します.
54            ここで,行列<literal>[A1,B1,C1,D1]</literal>は
55            その伝達関数<literal>H1(s)=C1*inv(s*eye()-A1)*B1+D1</literal>が
56            <literal>H(z)=C*inv(z*eye()-A)*B+D</literal>において
57            <literal>z</literal>を<literal>z=(a*s+b)/(c*s+d)</literal>で置換することにより
58            得られたものです.
59            <literal>w=bilin(bilin(w,[a,b,c,d]),[d,-b,-c,a])</literal>の関係があります.
60        </para>
61    </refsection>
62    <refsection>
63        <title>例</title>
64        <programlisting role="example"><![CDATA[
65s=poly(0,'s');z=poly(0,'z');
66w=ssrand(1,1,3);
67wtf=ss2tf(w);v=[2,3,-1,4];a=v(1);b=v(2);c=v(3);d=v(4);
68[horner(wtf,(a*z+b)/(c*z+d)),ss2tf(bilin(w,[a,b,c,d]))]
69clean(ss2tf(bilin(bilin(w,[a,b,c,d]),[d,-b,-c,a]))-wtf)
70 ]]></programlisting>
71    </refsection>
72    <refsection role="see also">
73        <title>参照</title>
74        <simplelist type="inline">
75            <member>
76                <link linkend="horner">horner</link>
77            </member>
78            <member>
79                <link linkend="cls2dls">cls2dls</link>
80            </member>
81        </simplelist>
82    </refsection>
83</refentry>
84