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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/ss2ss.xml
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<?xml version="1.0" encoding="UTF-8"?>
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<!--
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 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
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 * Copyright (C) INRIA - 
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 * 
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 * This file must be used under the terms of the CeCILL.
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 * This source file is licensed as described in the file COPYING, which
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 * you should have received as part of this distribution.  The terms
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 * are also available at    
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 * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
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 *
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 -->
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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:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:id="ss2ss" xml:lang="en">
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  <refnamediv>
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    <refname>ss2ss</refname>
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    <refpurpose>state-space to state-space conversion, feedback,
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      injection
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    </refpurpose>
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  </refnamediv>
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  <refsynopsisdiv>
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    <title>Calling Sequence</title>
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    <synopsis>[Sl1,right,left]=ss2ss(Sl,T, [F, [G , [flag]]])</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>Sl</term>
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        <listitem>
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          <para>
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            linear system (<literal>syslin</literal> list) in state-space
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            form
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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>T</term>
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        <listitem>
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          <para>square (non-singular) matrix</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>Sl1, right, left</term>
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        <listitem>
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          <para>linear systems (syslin lists) in state-space form</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>F</term>
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        <listitem>
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          <para>real matrix (state feedback gain)</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>G</term>
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        <listitem>
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          <para>real matrix (output injection gain)</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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      Returns the linear system <literal>Sl1=[A1,B1,C1,D1]</literal> where
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      <literal>A1=inv(T)*A*T, B1=inv(T)*B, C1=C*T, D1=D</literal>.
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    </para>
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    <para>
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      Optional parameters <literal>F</literal> and <literal>G</literal>
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      are state feedback and output injection respectively.
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    </para>
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    <para>
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      For example, <literal>Sl1=ss2ss(Sl,T,F)</literal> returns
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      <literal>Sl1</literal> with:
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    </para>
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    <mediaobject>
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      <imageobject>
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        <imagedata align="center" fileref="../mml/ss2ss_equation1.mml"/>
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      </imageobject>
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    </mediaobject>
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    <para>
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      and <literal>right</literal> is a non singular linear system such
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      that <literal>Sl1=Sl*right</literal>.
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    </para>
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    <para>
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      <literal>Sl1*inv(right)</literal> is a factorization of
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      <literal>Sl</literal>.
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    </para>
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    <para>
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      <literal>Sl1=ss2ss(Sl,T,0*F,G)</literal> returns
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      <literal>Sl1</literal> with:
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    </para>
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    <mediaobject>
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      <imageobject>
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        <imagedata align="center" fileref="../mml/ss2ss_equation2.mml"/>
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      </imageobject>
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    </mediaobject>
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    <para>
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      and <literal>left</literal> is a non singular linear system such
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      that <literal>Sl1=left*Sl</literal> (<literal>right=Id</literal> if
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      <literal>F=0</literal>).
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    </para>
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    <para>
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      When both <literal>F</literal> and <literal>G</literal> are given,
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      <literal>Sl1=left*Sl*right</literal>.
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    </para>
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    <itemizedlist>
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      <listitem>
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        <para>
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          When <literal>flag</literal> is used and
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          <literal>flag=1</literal> an output injection as follows is used
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        </para>
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        <mediaobject>
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          <imageobject>
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            <imagedata fileref="../mml/ss2ss_equation3.mml"/>
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          </imageobject>
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        </mediaobject>
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        <para>
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          and then a feedback is performed, <literal>F</literal> must be
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          of size <literal>(m+p,n)</literal>
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        </para>
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        <mediaobject>
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          <imageobject>
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            <imagedata align="left" fileref="../mml/ss2ss_equation4.mml"/>
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          </imageobject>
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        </mediaobject>
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        <para>
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          <literal>right</literal> and <literal>left</literal> have the
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          following property:
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        </para>
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        <programlisting role=""><![CDATA[ 
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Sl1 = left*sysdiag(sys,eye(p,p))*right 
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 ]]></programlisting>
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      </listitem>
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      <listitem>
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        <para>
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          When <literal>flag</literal> is used and
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          <literal>flag=2</literal> a feedback (<literal>F</literal> must be of
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          size <literal>(m,n)</literal>) is performed and then the above output
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          injection is applied. <literal>right</literal> and
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          <literal>left</literal> have the following property:
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        </para>
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        <programlisting role=""><![CDATA[ 
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 Sl1 = left*sysdiag(sys*right,eye(p,p)))
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 ]]></programlisting>
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      </listitem>
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    </itemizedlist>
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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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Sl=ssrand(2,2,5); trzeros(Sl)       // zeros are invariant:
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Sl1=ss2ss(Sl,rand(5,5),rand(2,5),rand(5,2)); 
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trzeros(Sl1), trzeros(rand(2,2)*Sl1*rand(2,2))
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// output injection [ A + GC, (B+GD,-G)]
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//                  [   C   , (D   , 0)]
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p=1,m=2,n=2; sys=ssrand(p,m,n);
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// feedback (m,n)  first and then output injection.
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F1=rand(m,n);
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G=rand(n,p);
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[sys1,right,left]=ss2ss(sys,rand(n,n),F1,G,2);
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// Sl1 equiv left*sysdiag(sys*right,eye(p,p)))
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res=clean(ss2tf(sys1) - ss2tf(left*sysdiag(sys*right,eye(p,p))))
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// output injection then feedback (m+p,n) 
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F2=rand(p,n); F=[F1;F2];
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[sys2,right,left]=ss2ss(sys,rand(n,n),F,G,1);
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// Sl1 equiv left*sysdiag(sys,eye(p,p))*right 
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res=clean(ss2tf(sys2)-ss2tf(left*sysdiag(sys,eye(p,p))*right))
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// when F2= 0; sys1 and sys2 are the same 
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F2=0*rand(p,n);F=[F1;F2];
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[sys2,right,left]=ss2ss(sys,rand(n,n),F,G,1);
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res=clean(ss2tf(sys2)-ss2tf(sys1))
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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="projsl">projsl</link>
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      </member>
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      <member>
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        <link linkend="feedback">feedback</link>
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      </member>
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    </simplelist>
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  </refsection>
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</refentry>