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[scilab.git] / scilab / modules / cacsd / help / en_US / formal_representation / des2tf.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="en" xml:id="des2tf">
17     <refnamediv>
18         <refname>des2tf</refname>
19         <refpurpose>descriptor to transfer function conversion</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Calling Sequence</title>
23         <synopsis>[S]=des2tf(sl)
24             [Bfs,Bis,chis]=des2tf(sl)
25         </synopsis>
26     </refsynopsisdiv>
27     <refsection>
28         <title>Arguments</title>
29         <variablelist>
30             <varlistentry>
31                 <term>sl</term>
32                 <listitem>
33                     <para>list (linear system in descriptor form)</para>
34                 </listitem>
35             </varlistentry>
36             <varlistentry>
37                 <term>Bfs, Bis</term>
38                 <listitem>
39                     <para>two polynomial matrices</para>
40                 </listitem>
41             </varlistentry>
42             <varlistentry>
43                 <term>chis</term>
44                 <listitem>
45                     <para>polynomial</para>
46                 </listitem>
47             </varlistentry>
48             <varlistentry>
49                 <term>S</term>
50                 <listitem>
51                     <para>rational matrix</para>
52                 </listitem>
53             </varlistentry>
54         </variablelist>
55     </refsection>
56     <refsection>
57         <title>Description</title>
58         <para>
59             Given the linear system in descriptor form i.e.
60             <literal>Sl=list('des',A,B,C,D,E)</literal>, <literal>des2tf</literal> converts <literal>sl</literal> into
61             its transfer function representation:
62         </para>
63         <programlisting role=""><![CDATA[ 
64 S=C*(s*E-A)^(-1)*B+D
65  ]]></programlisting>
66         <para>
67             Called with 3 outputs arguments <literal>des2tf</literal> returns
68             <literal>Bfs</literal> and <literal>Bis</literal> two polynomial matrices, and <literal>chis</literal>
69             polynomial such that:
70         </para>
71         <programlisting role=""><![CDATA[ 
72 S=Bfs/chis - Bis
73  ]]></programlisting>
74         <para>
75             <literal>chis</literal> is the determinant of <literal>(s*E-A)</literal> (up to a xcative constant);
76         </para>
77     </refsection>
78     <refsection>
79         <title>Examples</title>
80         <programlisting role="example"><![CDATA[ 
81 s=poly(0,'s');
82 G=[1/(s+1),s;1+s^2,3*s^3];
83 Descrip=tf2des(G);Tf1=des2tf(Descrip)
84 Descrip2=tf2des(G,"withD");Tf2=des2tf(Descrip2)
85 [A,B,C,D,E]=Descrip2(2:6);Tf3=C*inv(s*E-A)*B+D
86  ]]></programlisting>
87     </refsection>
88     <refsection role="see also">
89         <title>See Also</title>
90         <simplelist type="inline">
91             <member>
92                 <link linkend="glever">glever</link>
93             </member>
94             <member>
95                 <link linkend="pol2des">pol2des</link>
96             </member>
97             <member>
98                 <link linkend="tf2des">tf2des</link>
99             </member>
100             <member>
101                 <link linkend="ss2tf">ss2tf</link>
102             </member>
103             <member>
104                 <link linkend="des2ss">des2ss</link>
105             </member>
106             <member>
107                 <link linkend="rowshuff">rowshuff</link>
108             </member>
109         </simplelist>
110     </refsection>
111 </refentry>