<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) INRIA -
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
 * along with this program.
 *
 -->
<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>Syntax</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>
