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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="zeropen">
<refnamediv>
<refname>zeropen</refname>
<refpurpose>zero pencil</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[Z,U]=zeropen(Sl)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>Sl</term>
<listitem>
<para>
a linear system (<literal>syslin</literal> list in state-space form <literal>[A,B,C,D]</literal>)
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Z</term>
<listitem>
<para>
matrix pencil <literal>Z=s*E-A</literal>
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>U</term>
<listitem>
<para>square orthogonal matrix</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>Z= sE - F</literal> is the zero pencil of the linear system <literal>Sl</literal> with
matrices <literal>[A,B,C,D]</literal>. Utility function.
</para>
<para>
With <literal>U</literal> row compression of <literal>[B;D]</literal> i.e, <literal>U*[B;D]=[0;*]</literal>; one has:
</para>
<programlisting role=""><![CDATA[
U*[-sI+A |B; [ Z |0;
C |D] = [ * |*]
]]></programlisting>
<para>
The zeros of <literal>Z</literal> are the zeros of <literal>Sl</literal>.
</para>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="systmat">systmat</link>
</member>
<member>
<link linkend="kroneck">kroneck</link>
</member>
</simplelist>
</refsection>
</refentry>
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