21d77eaeec064c20a749c1b2910aec0544b7a5cf
[scilab.git] / scilab / modules / elementary_functions / help / en_US / signalprocessing / syslin.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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13 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:id="syslin" xml:lang="en">
14   <info>
15     <pubdate>$LastChangedDate$</pubdate>
16   </info>
17   <refnamediv>
18     <refname>syslin</refname>
19     <refpurpose>linear system definition</refpurpose>
20   </refnamediv>
21   <refsynopsisdiv>
22     <title>Calling Sequence</title>
23     <synopsis>[sl]=syslin(dom,A,B,C [,D [,x0] ])
24 [sl]=syslin(dom,N,D)
25 [sl]=syslin(dom,H)</synopsis>
26   </refsynopsisdiv>
27   <refsection>
28     <title>Arguments</title>
29     <variablelist>
30       <varlistentry>
31         <term>dom</term>
32         <listitem>
33           <para>character string (<literal>'c'</literal>,
34           <literal>'d'</literal>), or <literal>[]</literal> or a
35           scalar.</para>
36         </listitem>
37       </varlistentry>
38       <varlistentry>
39         <term>A,B,C,D</term>
40         <listitem>
41           <para>matrices of the state-space representation
42           (<literal>D</literal> optional with default value zero matrix). For
43           improper systems <literal>D</literal> is a polynomial matrix.</para>
44         </listitem>
45       </varlistentry>
46       <varlistentry>
47         <term>x0</term>
48         <listitem>
49           <para>vector (initial state; default value is
50           <literal>0</literal>)</para>
51         </listitem>
52       </varlistentry>
53       <varlistentry>
54         <term>N, D</term>
55         <listitem>
56           <para>polynomial matrices</para>
57         </listitem>
58       </varlistentry>
59       <varlistentry>
60         <term>H</term>
61         <listitem>
62           <para>rational matrix or linear state space representation</para>
63         </listitem>
64       </varlistentry>
65       <varlistentry>
66         <term>sl</term>
67         <listitem>
68           <para>tlist ("<literal>syslin</literal>" list) representing the
69           linear system</para>
70         </listitem>
71       </varlistentry>
72     </variablelist>
73   </refsection>
74   <refsection>
75     <title>Description</title>
76     <para><literal>syslin</literal> defines a linear system as a list and
77     checks consistency of data.</para>
78     <para><literal>dom</literal> specifies the time domain of the system and
79     can have the following values:</para>
80     <para><literal>dom='c'</literal> for a continuous time system,
81     <literal>dom='d'</literal> for a discrete time system,
82     <literal>n</literal> for a sampled system with sampling period
83     <literal>n</literal> (in seconds).</para>
84     <para><literal>dom=[]</literal> if the time domain is undefined</para>
85     <para>State-space representation:</para>
86     <programlisting><![CDATA[ 
87 sl=syslin(dom,A,B,C [,D [,x0] ])
88  ]]></programlisting>
89     <para>represents the system :</para>
90     <informalequation>
91       <mediaobject>
92         <imageobject>
93           <imagedata align="center" fileref="../../mml/syslin_equation_1.mml"/>
94         </imageobject>
95       </mediaobject>
96     </informalequation>
97     <para>The output of <literal>syslin</literal> is a list of the following
98     form:
99     <literal>sl=tlist(['lss','A','B','C','D','X0','dt'],A,B,C,D,x0,dom)</literal>
100     Note that <literal>D</literal> is allowed to be a polynomial matrix
101     (improper systems).</para>
102     <para>Transfer matrix representation:</para>
103     <programlisting><![CDATA[ 
104 sl=syslin(dom,N,D) 
105 sl=syslin(dom,H)
106  ]]></programlisting>
107     <para>The output of <literal>syslin</literal> is a list of the following
108     form : <literal>sl=tlist(['r','num','den','dt'],N,D,dom)</literal> or
109     <literal>sl=tlist(['r','num','den','dt'],H(2),H(3),dom)</literal>.</para>
110     <para>Linear systems defined as <literal>syslin</literal> can be
111     manipulated as usual matrices (concatenation, extraction, transpose,
112     multiplication, etc) both in state-space or transfer
113     representation.</para>
114     <para>Most of state-space control functions receive a
115     <literal>syslin</literal> list as input instead of the four matrices
116     defining the system.</para>
117   </refsection>
118   <refsection>
119     <title>Examples</title>
120     <programlisting role="example"><![CDATA[ 
121 A=[0,1;0,0];B=[1;1];C=[1,1];
122 S1=syslin('c',A,B,C)   //Linear system definition
123 S1("A")    //Display of A-matrix
124 S1("X0"), S1("dt") // Display of X0 and time domain
125 s=poly(0,'s');
126 D=s;
127 S2=syslin('c',A,B,C,D)
128 H1=(1+2*s)/s^2, S1bis=syslin('c',H1)
129 H2=(1+2*s+s^3)/s^2, S2bis=syslin('c',H2)
130 S1+S2
131 [S1,S2]
132 ss2tf(S1)-S1bis
133 S1bis+S2bis
134 S1*S2bis
135 size(S1)
136  ]]></programlisting>
137   </refsection>
138   <refsection role="see also">
139     <title>See Also</title>
140     <simplelist type="inline">
141       <member>
142         <link linkend="tlist">tlist</link>
143       </member>
144       <member>
145         <link linkend="lsslist">lsslist</link>
146       </member>
147       <member>
148         <link linkend="rlist">rlist</link>
149       </member>
150       <member>
151         <link linkend="ssrand">ssrand</link>
152       </member>
153       <member>
154         <link linkend="ss2tf">ss2tf</link>
155       </member>
156       <member>
157         <link linkend="tf2ss">tf2ss</link>
158       </member>
159       <member>
160         <link linkend="dscr">dscr</link>
161       </member>
162       <member>
163         <link linkend="abcd">abcd</link>
164       </member>
165     </simplelist>
166   </refsection>
167 </refentry>