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[scilab.git] / scilab / modules / cacsd / help / ja_JP / cainv.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="cainv">
17     <refnamediv>
18         <refname>cainv</refname>
19         <refpurpose>abinvの双対</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>呼び出し手順</title>
23         <synopsis>[X,dims,J,Y,k,Z]=cainv(Sl,alfa,beta,flag)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>パラメータ</title>
27         <variablelist>
28             <varlistentry>
29                 <term>Sl</term>
30                 <listitem>
31                     <para>
32                         行列 <literal>[A,B,C,D]</literal>を含む<literal>syslin</literal> リスト.
33                     </para>
34                 </listitem>
35             </varlistentry>
36             <varlistentry>
37                 <term>alfa</term>
38                 <listitem>
39                     <para>実数の数値またはベクトル (複素数となる場合もある,閉ループ極の位置)</para>
40                 </listitem>
41             </varlistentry>
42             <varlistentry>
43                 <term>beta</term>
44                 <listitem>
45                     <para>実数の数値またはベクトル (複素数となる場合もある,閉ループ極の位置)</para>
46                 </listitem>
47             </varlistentry>
48             <varlistentry>
49                 <term>flag</term>
50                 <listitem>
51                     <para>
52                         (オプションの) 文字列 <literal>'ge'</literal> (default)または <literal>'st'</literal> または <literal>'pp'</literal>
53                     </para>
54                 </listitem>
55             </varlistentry>
56             <varlistentry>
57                 <term>X</term>
58                 <listitem>
59                     <para>大きさ nx (状態空間の次元)の直交行列.</para>
60                 </listitem>
61             </varlistentry>
62             <varlistentry>
63                 <term>dims</term>
64                 <listitem>
65                     <para>
66                         整数行ベクトル <literal>dims=[nd1,nu1,dimS,dimSg,dimN]</literal>  (5エントリ
67                         , 非降順).
68                         <literal>flag='st'</literal>
69                         (もしくは<literal>'pp'</literal>)の場合, <literal>dims</literal> は 4 
70                         (もしくは3)個の要素を有します.
71                     </para>
72                 </listitem>
73             </varlistentry>
74             <varlistentry>
75                 <term>J</term>
76                 <listitem>
77                     <para>実数行列 (出力)</para>
78                 </listitem>
79             </varlistentry>
80             <varlistentry>
81                 <term>Y</term>
82                 <listitem>
83                     <para>大きさnyの直交行列 (出力空間の次元).</para>
84                 </listitem>
85             </varlistentry>
86             <varlistentry>
87                 <term>k</term>
88                 <listitem>
89                     <para>
90                         整数 (<literal>Sl</literal>のランク)
91                     </para>
92                 </listitem>
93             </varlistentry>
94             <varlistentry>
95                 <term>Z</term>
96                 <listitem>
97                     <para>
98                         正則な線形システム (<literal>syslin</literal> リスト)
99                     </para>
100                 </listitem>
101             </varlistentry>
102         </variablelist>
103     </refsection>
104     <refsection>
105         <title>説明</title>
106         <para>
107             <literal>cainv</literal> は
108             (状態空間および出力状態応答の)基底 <literal>(X,Y)</literal>を見つけます.
109             基底を (X,Y)とする行列 Slは以下のように表示されます:
110         </para>
111         <programlisting role=""><![CDATA[ 
112                [A11,*,*,*,*,*]                [*]
113                [0,A22,*,*,*,*]                [*]
114 X'*(A+J*C)*X = [0,0,A33,*,*,*]   X'*(B+J*D) = [*]
115                [0,0,0,A44,*,*]                [0]
116                [0,0,0,0,A55,*]                [0]
117                [0,0,0,0,0,A66]                [0]
118        Y*C*X = [0,0,C13,*,*,*]          Y*D = [*]
119                [0,0,0,0,0,C26]                [0]
120  ]]></programlisting>
121         <para>
122             The partition of <literal>X</literal>の分割は
123             ベクトル<literal>dims=[nd1,nu1,dimS,dimSg,dimN]</literal>により定義され,
124             <literal>Y</literal>の分割は<literal>k</literal>により定義されます.
125         </para>
126         <para>
127             <literal>A11</literal><literal>(nd1 x nd1)</literal> の固有値は不安定です.
128             <literal>A22</literal> <literal>(nu1-nd1 x nu1-nd1)</literal>の固有値は安定です.
129         </para>
130         <para>
131             対 <literal>(A33, C13)</literal> <literal>(dimS-nu1 x dimS-nu1, k x dimS-nu1)</literal>は
132             可観測, <literal>A33</literal>の固有値は <literal>alfa</literal>に設定されます.
133         </para>
134         <para>
135             行列 <literal>A44</literal> <literal>(dimSg-dimS x dimSg-dimS)</literal> は不安定です.
136             行列 <literal>A55</literal> <literal>(dimN-dimSg,dimN-dimSg)</literal> は安定です.
137         </para>
138         <para>
139             対 <literal>(A66,C26)</literal> <literal>(nx-dimN x nx-dimN)</literal> は可観測, 
140             <literal>A66</literal>の固有値は<literal>beta</literal>に設定されます.
141         </para>
142         <para>
143             <literal>X</literal>の最初の<literal>dimS</literal>列は,
144             Im(B)を含む不変部分空間 S= smallest (C,A) に広がり,
145             <literal>X</literal>の最初の<literal>dimSg</literal>列は,
146             <literal>Sl</literal>の最大"相補可検出部分空間" Sg に広がります.
147         </para>
148         <para>
149             <literal>X</literal>の最初の<literal>dimN</literal>列は,
150             <literal>Sl</literal> の最大"相補可観測部分空間"に広がります.
151             (B(ker(D))=0の場合,<literal>dimS=0</literal>)
152         </para>
153         <para>
154             <literal>flag='st'</literal> が指定された場合,
155             5個の分割ブロック行列が返され,
156             <literal>dims</literal>は4つの要素を有します.
157             <literal>flag='pp'</literal>が指定された場合,
158             4個の分割ブロックが返されます(abinv参照).
159         </para>
160         <para>
161             この関数は次のように未知入力オブザーバを計算する際に使用することができます:
162         </para>
163         <programlisting role=""><![CDATA[ 
164 // DDEP: dot(x)=A x + Bu + Gd
165 //           y= Cx   (observation)
166 //           z= Hx    (z=variable to be estimated, d=disturbance)
167 //  Find: dot(w) = Fw + Ey + Ru such that
168 //          zhat = Mw + Ny
169 //           z-Hx goes to zero at infinity
170 //  Solution exists iff Ker H contains Sg(A,C,G) inter KerC (assuming detectability)
171 //i.e. H is such that:
172 // For any W which makes a column compression of [Xp(1:dimSg,:);C]
173 // with Xp=X' and [X,dims,J,Y,k,Z]=cainv(syslin('c',A,G,C));
174 // [Xp(1:dimSg,:);C]*W = [0 | *] one has
175 // H*W = [0 | *]  (with at least as many aero columns as above).
176  ]]></programlisting>
177     </refsection>
178     <refsection role="see also">
179         <title>参照</title>
180         <simplelist type="inline">
181             <member>
182                 <link linkend="abinv">abinv</link>
183             </member>
184             <member>
185                 <link linkend="dt_ility">dt_ility</link>
186             </member>
187             <member>
188                 <link linkend="ui_observer">ui_observer</link>
189             </member>
190         </simplelist>
191     </refsection>
192 </refentry>