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  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/cacsd/help/en_US/fstabst.xml
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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" version="5.0-subset Scilab" xml:lang="en" xml:id="fstabst">
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  <refnamediv>
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    <refname>fstabst</refname>
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    <refpurpose>Youla's parametrization of continuous time linear dynmaical systems</refpurpose>
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  </refnamediv>
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  <refsynopsisdiv>
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    <title>Calling Sequence</title>
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    <synopsis>J = fstabst(P,r)</synopsis>
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  </refsynopsisdiv>
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  <refsection>
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    <title>Arguments</title>
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    <variablelist>
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      <varlistentry>
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        <term>P</term>
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        <listitem>
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          <para>a continuous time linear dynamical system.</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>r</term>
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        <listitem>
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          <para>
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            1x2 row vector, dimension of <literal>P22</literal>
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          </para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>J</term>
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        <listitem>
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          <para>
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            a continuous time linear dynamical system (with same representation as <literal>P</literal>.
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          </para>
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        </listitem>
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      </varlistentry>
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    </variablelist>
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  </refsection>
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  <refsection>
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    <title>Description</title>
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    <para>
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      Parameterization of all stabilizing feedbacks.
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    </para>
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    <para>
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      <literal>P</literal> is partitioned as follows:
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    </para>
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    <programlisting role=""><![CDATA[ 
 
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    <refnamediv>
 
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        <refname>fstabst</refname>
 
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        <refpurpose>Youla's parametrization of continuous time linear dynmaical systems</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>J = fstabst(P,r)</synopsis>
 
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    </refsynopsisdiv>
 
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    <refsection>
 
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        <title>Arguments</title>
 
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        <variablelist>
 
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            <varlistentry>
 
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                <term>P</term>
 
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                <listitem>
 
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                    <para>a continuous time linear dynamical system.</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>r</term>
 
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                <listitem>
 
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                    <para>
 
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                        1x2 row vector, dimension of <literal>P22</literal>
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>J</term>
 
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                <listitem>
 
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                    <para>
 
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                        a continuous time linear dynamical system (with same representation as <literal>P</literal>.
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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        </variablelist>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Description</title>
 
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        <para>
 
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            Parameterization of all stabilizing feedbacks.
 
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        </para>
 
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        <para>
 
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            <literal>P</literal> is partitioned as follows:
 
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        </para>
 
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        <programlisting role=""><![CDATA[ 
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P=[ P11 P12;
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    P21 P22]  
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 ]]></programlisting>
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    <para>
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      (in state-space or transfer form: automatic conversion in state-space is
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      done for the computations)
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    </para>
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    <para>
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      <literal>r</literal> = size of  <literal>P22</literal> subsystem, (2,2) block of <literal>P</literal>
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    </para>
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    <programlisting role=""><![CDATA[ 
 
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        <para>
 
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            (in state-space or transfer form: automatic conversion in state-space is
 
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            done for the computations)
 
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        </para>
 
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        <para>
 
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            <literal>r</literal> = size of  <literal>P22</literal> subsystem, (2,2) block of <literal>P</literal>
 
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        </para>
 
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        <programlisting role=""><![CDATA[ 
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J =[J11 J12;
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    J21 J22]
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 ]]></programlisting>
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    <para>
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      <literal>K</literal> is a stabilizing controller for <literal>P</literal> (i.e. <literal>P22</literal>) iff 
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      <literal>K=lft(J,r,Q)</literal> with <literal>Q</literal> stable.
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    </para>
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    <para>
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      The central part of <literal>J</literal> , <literal>J11</literal> is the lqg regulator for <literal>P</literal>
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    </para>
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    <para>
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      This <literal>J</literal> is such that defining <literal>T</literal> as the 2-port <literal>lft</literal> of <literal>P</literal>
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      and <literal>J</literal> : <literal>[T,rt]=lft(P,r,J,r)</literal> one has that <literal>T12</literal> is inner
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      and <literal>T21</literal> is co-inner.
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    </para>
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  </refsection>
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  <refsection>
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    <title>Examples</title>
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    <programlisting role="example"><![CDATA[ 
 
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        <para>
 
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            <literal>K</literal> is a stabilizing controller for <literal>P</literal> (i.e. <literal>P22</literal>) iff 
 
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            <literal>K=lft(J,r,Q)</literal> with <literal>Q</literal> stable.
 
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        </para>
 
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        <para>
 
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            The central part of <literal>J</literal> , <literal>J11</literal> is the lqg regulator for <literal>P</literal>
 
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        </para>
 
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        <para>
 
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            This <literal>J</literal> is such that defining <literal>T</literal> as the 2-port <literal>lft</literal> of <literal>P</literal>
 
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            and <literal>J</literal> : <literal>[T,rt]=lft(P,r,J,r)</literal> one has that <literal>T12</literal> is inner
 
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            and <literal>T21</literal> is co-inner.
 
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        </para>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Examples</title>
 
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        <programlisting role="example"><![CDATA[ 
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ny=2;nu=3;nx=4;
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P22=ssrand(ny,nu,nx);
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bigQ=rand(nx+nu,nx+nu);bigQ=bigQ*bigQ';
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K=lft(J,r,Q);
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A=h_cl(P,r,K); spec(A)
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 ]]></programlisting>
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  </refsection>
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  <refsection role="see also">
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    <title>See Also</title>
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    <simplelist type="inline">
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      <member>
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        <link linkend="obscont">obscont</link>
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      </member>
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      <member>
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        <link linkend="lft">lft</link>
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      </member>
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      <member>
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        <link linkend="lqg">lqg</link>
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      </member>
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      <member>
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        <link linkend="lqg2stan">lqg2stan</link>
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      </member>
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    </simplelist>
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  </refsection>
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  <refsection>
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    <title>History</title>
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    <revhistory>
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      <revision>
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        <revnumber>5.4.0</revnumber>
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        <revremark>
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          <literal>Sl</literal> is now checked for
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          continuous time linear dynamical system.  This modification
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          has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
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        </revremark>
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      </revision>
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    </revhistory>
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  </refsection>
 
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    </refsection>
 
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    <refsection role="see also">
 
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        <title>See Also</title>
 
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        <simplelist type="inline">
 
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            <member>
 
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                <link linkend="obscont">obscont</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="lft">lft</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="lqg">lqg</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="lqg2stan">lqg2stan</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
 
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    <refsection>
 
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        <title>History</title>
 
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        <revhistory>
 
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            <revision>
 
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                <revnumber>5.4.0</revnumber>
 
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                <revremark>
 
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                    <literal>Sl</literal> is now checked for
 
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                    continuous time linear dynamical system.  This modification
 
124
                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
 
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                </revremark>
 
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            </revision>
 
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        </revhistory>
 
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    </refsection>
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</refentry>