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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
*
-->
<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" xmlns:scilab="http://www.scilab.org" xml:id="syslin" xml:lang="en">
<refnamediv>
<refname>syslin</refname>
<refpurpose>linear system definition</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[sl]=syslin(dom,A,B,C [,D [,x0] ])
[sl]=syslin(dom,N,D)
[sl]=syslin(dom,H)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>dom</term>
<listitem>
<para>
character string (<literal>'c'</literal>,
<literal>'d'</literal>), or <literal>[]</literal> or a
scalar.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>A,B,C,D</term>
<listitem>
<para>matrices of the state-space representation
(<literal>D</literal> optional with default value zero matrix). For
improper systems <literal>D</literal> is a polynomial matrix.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>x0</term>
<listitem>
<para>vector (initial state; default value is
<literal>0</literal>)
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>N, D</term>
<listitem>
<para>polynomial matrices</para>
</listitem>
</varlistentry>
<varlistentry>
<term>H</term>
<listitem>
<para>rational matrix or linear state space representation</para>
</listitem>
</varlistentry>
<varlistentry>
<term>sl</term>
<listitem>
<para>
tlist ("<literal>syslin</literal>" list) representing the
linear system
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>syslin</literal> defines a linear system as a list and
checks consistency of data.
</para>
<para>
<literal>dom</literal> specifies the time domain of the system and
can have the following values:
</para>
<para>
<literal>dom='c'</literal> for a continuous time system,
<literal>dom='d'</literal> for a discrete time system,
<literal>n</literal> for a sampled system with sampling period
<literal>n</literal> (in seconds).
</para>
<para>
<literal>dom=[]</literal> if the time domain is undefined
</para>
<para>State-space representation:</para>
<programlisting><![CDATA[
sl=syslin(dom,A,B,C [,D [,x0] ])
]]></programlisting>
<para>represents the system :</para>
<informalequation>
<mediaobject>
<imageobject>
<imagedata align="center" fileref="../mml/syslin_equation_1.mml"/>
</imageobject>
</mediaobject>
</informalequation>
<para>
The output of <literal>syslin</literal> is a list of the following
form:
<literal>sl=tlist(['lss','A','B','C','D','X0','dt'],A,B,C,D,x0,dom)</literal>
Note that <literal>D</literal> is allowed to be a polynomial matrix
(improper systems).
</para>
<para>Transfer matrix representation:</para>
<programlisting><![CDATA[
sl=syslin(dom,N,D)
sl=syslin(dom,H)
]]></programlisting>
<para>
The output of <literal>syslin</literal> is a list of the following
form : <literal>sl = rlist(N,D,dom)</literal> or
<literal>sl=rlist(H(2),H(3),dom)</literal>.
</para>
<para>
Linear systems defined as <literal>syslin</literal> can be
manipulated as usual matrices (concatenation, extraction, transpose,
multiplication, etc) both in state-space or transfer
representation.
</para>
<para>Most of state-space control functions receive a
<literal>syslin</literal> list as input instead of the four matrices
defining the system.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
A=[0,1;0,0];B=[1;1];C=[1,1];
S1=syslin('c',A,B,C) //Linear system definition
S1("A") //Display of A-matrix
S1("X0"), S1("dt") // Display of X0 and time domain
s=poly(0,'s');
D=s;
S2=syslin('c',A,B,C,D)
H1=(1+2*s)/s^2, S1bis=syslin('c',H1)
H2=(1+2*s+s^3)/s^2, S2bis=syslin('c',H2)
S1+S2
[S1,S2]
ss2tf(S1)-S1bis
S1bis+S2bis
S1*S2bis
size(S1)
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="tlist">tlist</link>
</member>
<member>
<link linkend="lsslist">lsslist</link>
</member>
<member>
<link linkend="rlist">rlist</link>
</member>
<member>
<link linkend="ssrand">ssrand</link>
</member>
<member>
<link linkend="ss2tf">ss2tf</link>
</member>
<member>
<link linkend="tf2ss">tf2ss</link>
</member>
<member>
<link linkend="dscr">dscr</link>
</member>
<member>
<link linkend="abcd">abcd</link>
</member>
</simplelist>
</refsection>
</refentry>
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