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[scilab.git] / scilab / modules / cacsd / help / en_US / bilin.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="bilin">
17     <refnamediv>
18         <refname>bilin</refname>
19         <refpurpose>general bilinear transform</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Calling Sequence</title>
23         <synopsis>[sl1]=bilin(sl,v)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Arguments</title>
27         <variablelist>
28             <varlistentry>
29                 <term>sl,sl1</term>
30                 <listitem>
31                     <para>
32                         linear systems (<literal>syslin</literal> lists)
33                     </para>
34                 </listitem>
35             </varlistentry>
36             <varlistentry>
37                 <term>v</term>
38                 <listitem>
39                     <para>
40                         real vector with 4 entries (<literal>v=[a,b,c,d]</literal>)
41                     </para>
42                 </listitem>
43             </varlistentry>
44         </variablelist>
45     </refsection>
46     <refsection>
47         <title>Description</title>
48         <para>
49             Given a linear system in state space form, <literal>sl=syslin(dom,A,B,C,D)</literal> 
50             (<literal>syslin</literal> list), <literal>sl1=bilin(sl,v)</literal>  returns in <literal>sl1</literal> a 
51             linear system with matrices <literal>[A1,B1,C1,D1]</literal> such that
52             the transfer function <literal>H1(s)=C1*inv(s*eye()-A1)*B1+D1</literal> is
53             obtained from <literal>H(z)=C*inv(z*eye()-A)*B+D</literal> by replacing <literal>z</literal>
54             by <literal>z=(a*s+b)/(c*s+d)</literal>.
55             One has <literal>w=bilin(bilin(w,[a,b,c,d]),[d,-b,-c,a])</literal>
56         </para>
57     </refsection>
58     <refsection>
59         <title>Examples</title>
60         <programlisting role="example"><![CDATA[ 
61 s=poly(0,'s');z=poly(0,'z');
62 w=ssrand(1,1,3);
63 wtf=ss2tf(w);v=[2,3,-1,4];a=v(1);b=v(2);c=v(3);d=v(4);
64 [horner(wtf,(a*z+b)/(c*z+d)),ss2tf(bilin(w,[a,b,c,d]))]
65 clean(ss2tf(bilin(bilin(w,[a,b,c,d]),[d,-b,-c,a]))-wtf)
66  ]]></programlisting>
67     </refsection>
68     <refsection role="see also">
69         <title>See Also</title>
70         <simplelist type="inline">
71             <member>
72                 <link linkend="horner">horner</link>
73             </member>
74             <member>
75                 <link linkend="cls2dls">cls2dls</link>
76             </member>
77         </simplelist>
78     </refsection>
79 </refentry>