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[scilab.git] / scilab / modules / cacsd / help / ja_JP / contr.xml
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="contr">
17     <refnamediv>
18         <refname>contr</refname>
19         <refpurpose>可制御性, 可制御部分空間, 階段化</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>呼び出しの手順</title>
23         <synopsis>n=contr(A,B [,tol])
24             [n,U]=contr(A,B [,tol])
25             [n,U,ind,V,Ac,Bc]=contr(A,B,[,tol])
26         </synopsis>
27     </refsynopsisdiv>
28     <refsection>
29         <title>パラメータ</title>
30         <variablelist>
31             <varlistentry>
32                 <term>A, B</term>
33                 <listitem>
34                     <para>実数行列</para>
35                 </listitem>
36             </varlistentry>
37             <varlistentry>
38                 <term>tol</term>
39                 <listitem>
40                     <para>虚数パラメータ</para>
41                 </listitem>
42             </varlistentry>
43             <varlistentry>
44                 <term>n</term>
45                 <listitem>
46                     <para>可制御部分空間の次元.</para>
47                 </listitem>
48             </varlistentry>
49             <varlistentry>
50                 <term>U</term>
51                 <listitem>
52                     <para>
53                         <literal>(A,B)</literal>を正準形に変換する直交変換基底.
54                     </para>
55                 </listitem>
56             </varlistentry>
57             <varlistentry>
58                 <term>V</term>
59                 <listitem>
60                     <para>制御空間の基底を変更する直交行列.</para>
61                 </listitem>
62             </varlistentry>
63             <varlistentry>
64                 <term>Ac</term>
65                 <listitem>
66                     <para>
67                         ブロックヘッセ行列 <literal>Ac=U'*A*U</literal>
68                     </para>
69                 </listitem>
70             </varlistentry>
71             <varlistentry>
72                 <term>Bc</term>
73                 <listitem>
74                     <para>
75                         is <literal>U'*B*V</literal>.
76                     </para>
77                 </listitem>
78             </varlistentry>
79             <varlistentry>
80                 <term>ind</term>
81                 <listitem>
82                     <para>
83                         可制御インデックス
84                         (サブスペース <literal>B, B+A*B,...=ind(1),ind(1)+ind(2),...</literal>の次元)
85                         を有するp整数ベクトル
86                     </para>
87                 </listitem>
88             </varlistentry>
89         </variablelist>
90     </refsection>
91     <refsection>
92         <title>説明</title>
93         <para>
94             <literal>[n,[U]]=contr(A,B,[tol])</literal> は
95             <literal>(A,B)</literal> の可制御形式を与える.
96             (<literal>dx/dt = A x + B u</literal> または
97             <literal>x(n+1) = A x(n) +b u(n)</literal>).
98             <literal>U</literal> の最初の <literal>n</literal> 列は、
99             可制御サブスペースの基底を構成する.
100         </para>
101         <para>
102             <literal>V=U(:,1:n)</literal>の場合, 
103             <literal>V'*A*V</literal> と <literal>V'*B</literal> は
104             <literal>(A,B)</literal> の可制御部を与える.
105         </para>
106         <para>
107             <literal>(Bc, Ac)</literal> は階段化可制御形式である.
108         </para>
109         <programlisting role=""><![CDATA[ 
110                    |B |sI-A      *  . . .  *      *       |
111                    | 1|    11       .      .      .       |
112                    |  |  A    sI-A    .    .      .       |
113                    |  |   21      22    .  .      .       |
114                    |  |        .     .     *      *       |
115 [U'BV|sI - U'AU] = |0 |     0    .     .                  |
116                    |  |            A     sI-A     *       |
117                    |  |             p,p-1    pp           |
118                    |  |                                   |
119                    |0 |         0          0   sI-A       |
120                    |  |                            p+1,p+1|
121  ]]></programlisting>
122     </refsection>
123     <refsection role="see also">
124         <title>参照</title>
125         <para>
126             Slicot ライブラリ (SCI/modules/cacsd/src/slicotのab01od参照).
127         </para>
128     </refsection>
129     <refsection>
130         <title>例</title>
131         <programlisting role="example"><![CDATA[ 
132 W=ssrand(2,3,5,list('co',3));  //cont. subspace has dim 3.
133 A=W("A");B=W("B");
134 [n,U]=contr(A,B);n
135 A1=U'*A*U;
136 spec(A1(n+1:$,n+1:$))  //uncontrollable modes
137 spec(A+B*rand(3,5))    
138  ]]></programlisting>
139     </refsection>
140     <refsection role="see also">
141         <title>参照</title>
142         <simplelist type="inline">
143             <member>
144                 <link linkend="canon">canon</link>
145             </member>
146             <member>
147                 <link linkend="cont_mat">cont_mat</link>
148             </member>
149             <member>
150                 <link linkend="unobs">unobs</link>
151             </member>
152             <member>
153                 <link linkend="stabil">stabil</link>
154             </member>
155             <member>
156                 <link linkend="st_ility">st_ility</link>
157             </member>
158         </simplelist>
159     </refsection>
160 </refentry>