<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( https://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="zeropen">
    <refnamediv>
        <refname>zeropen</refname>
        <refpurpose>zero pencil</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</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>
