<?xml version="1.0" encoding="UTF-8"?>
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<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="h_cl">
    <refnamediv>
        <refname>h_cl</refname>
        <refpurpose>closed loop matrix</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            Acl = h_cl(P, r, K)
            Acl = h_cl(P22, K)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>P, P22</term>
                <listitem>
                    <para>continuous time linear dynamical systems: augmented plant or nominal plant respectively</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>r</term>
                <listitem>
                    <para>
                        a two elements vector, dimensions of 2,2 part of <literal>P</literal> (<literal>r=[rows,cols]=size(P22)</literal>)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>K</term>
                <listitem>
                    <para>a continuous time linear dynamical system: the controller</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Acl</term>
                <listitem>
                    <para>real square matrix</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Given the standard plant <literal>P</literal> (with <literal>r=size(P22)</literal>) and the controller
            <literal>K</literal>, this function returns the closed loop matrix <literal>Acl</literal>.
        </para>
        <para>
            The poles of <literal>Acl</literal> must be stable for the internal stability
            of the closed loop system.
        </para>
        <para>
            <literal>Acl</literal> is the <literal>A</literal>-matrix of the linear system <literal>[I -P22;-K I]^-1</literal> i.e.
            the <literal>A</literal>-matrix of <literal>lft(P,r,K)</literal>
        </para>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="lft">lft</link>
            </member>
        </simplelist>
    </refsection>
    <refsection>
        <title>Authors</title>
        <para>F. D.  </para>
    </refsection>
    <refsection>
        <title>History</title>
        <revhistory>
            <revision>
                <revnumber>5.4.0</revnumber>
                <revremark>
                    <literal>Sl</literal> is now checked for
                    continuous time linear dynamical system.  This modification
                    has been introduced by this <ulink url="https://gitlab.com/scilab/scilab/-/commit/3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
                </revremark>
            </revision>
        </revhistory>
    </refsection>
</refentry>
