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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 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: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="dsimul">
<refnamediv>
<refname>dsimul</refname>
<refpurpose>state space discrete time simulation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>y=dsimul(sl,u)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>sl</term>
<listitem>
<para>
<literal>syslin</literal> list describing a discrete time linear system
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>u</term>
<listitem>
<para>real matrix of appropriate dimension</para>
</listitem>
</varlistentry>
<varlistentry>
<term>y</term>
<listitem>
<para>
output of <literal>sl</literal>
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Utility function.
If <literal>[A,B,C,D]=abcd(sl)</literal> and <literal>x0=sl('X0')</literal>, <literal>dsimul</literal> returns <literal>y=C*ltitr(A,B,u,x0)+D*u</literal> i.e.
the time response of <literal>sl</literal> to the input <literal>u</literal>.
<literal>sl</literal> is assumed to be in state space form (<literal>syslin</literal> list).
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
z=poly(0,'z');
h=(1-2*z)/(z^2-0.2*z+1);
sl=tf2ss(h);
u=zeros(1,20);u(1)=1;
x1=dsimul(sl,u) //Impulse response
u=ones(1,20);
x2=dsimul(sl,u); //Step response
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="syslin">syslin</link>
</member>
<member>
<link linkend="flts">flts</link>
</member>
<member>
<link linkend="ltitr">ltitr</link>
</member>
</simplelist>
</refsection>
</refentry>
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