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Viewing changes to modules/cacsd/help/en_US/st_ility.xml

  • 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/st_ility.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="st_ility">
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  <refnamediv>
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    <refname>st_ility</refname>
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    <refpurpose> stabilizability test</refpurpose>
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  </refnamediv>
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  <refsynopsisdiv>
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    <title>Calling Sequence</title>
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    <synopsis>[ns, [nc, [,U [,Slo] ]]]=st_ility(Sl [,tol])</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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            <literal>syslin</literal> list (linear system)
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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>ns</term>
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        <listitem>
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          <para> integer (dimension of stabilizable subspace)</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>nc</term>
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        <listitem>
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          <para>
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            integer (dimension of controllable subspace <literal>nc &lt;= ns</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>U</term>
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        <listitem>
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          <para>
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            basis such that its <literal>ns</literal> (resp. <literal>nc</literal>) first components span the stabilizable (resp. controllable) subspace
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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>Slo</term>
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        <listitem>
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          <para>
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            a linear system (<literal>syslin</literal> list)
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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>tol</term>
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        <listitem>
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          <para>threshold for controllability detection (see contr)</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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      <literal> Slo=( U'*A*U, U'*B, C*U, D, U'*x0 )</literal> (<literal>syslin</literal> list)
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      displays the stabilizable form of <literal>Sl</literal>. Stabilizability means
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      <literal>ns=nx</literal> (dim. of <literal>A</literal> matrix).
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    </para>
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    <programlisting role=""><![CDATA[ 
 
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    <refnamediv>
 
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        <refname>st_ility</refname>
 
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        <refpurpose> stabilizability test</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>[ns, [nc, [,U [,Slo] ]]]=st_ility(Sl [,tol])</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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                        <literal>syslin</literal> list (linear system)
 
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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>ns</term>
 
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                <listitem>
 
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                    <para> integer (dimension of stabilizable subspace)</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>nc</term>
 
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                <listitem>
 
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                    <para>
 
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                        integer (dimension of controllable subspace <literal>nc &lt;= ns</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>U</term>
 
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                <listitem>
 
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                    <para>
 
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                        basis such that its <literal>ns</literal> (resp. <literal>nc</literal>) first components span the stabilizable (resp. controllable) subspace
 
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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>Slo</term>
 
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                <listitem>
 
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                    <para>
 
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                        a linear system (<literal>syslin</literal> list)
 
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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>tol</term>
 
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                <listitem>
 
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                    <para>threshold for controllability detection (see contr)</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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            <literal> Slo=( U'*A*U, U'*B, C*U, D, U'*x0 )</literal> (<literal>syslin</literal> list)
 
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            displays the stabilizable form of <literal>Sl</literal>. Stabilizability means
 
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            <literal>ns=nx</literal> (dim. of <literal>A</literal> matrix).
 
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        </para>
 
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        <programlisting role=""><![CDATA[ 
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         [*,*,*]            [*]
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U'*A*U = [0,*,*]     U'*B = [0]
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         [0,0,*]            [0]
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 ]]></programlisting>
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    <para>
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      where <literal> (A11,B1) </literal> (dim(A11)= <literal>nc</literal>) is controllable and <literal>A22</literal> 
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      (dim(A22)=<literal>ns-nc</literal>) is stable.
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      "Stable" means real part of eigenvalues negative for a continuous
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      linear system, and magnitude of eigenvalues lower than one for a
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      discrete-time system (as defined by <literal>syslin</literal>).
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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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            where <literal> (A11,B1) </literal> (dim(A11)= <literal>nc</literal>) is controllable and <literal>A22</literal> 
 
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            (dim(A22)=<literal>ns-nc</literal>) is stable.
 
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            "Stable" means real part of eigenvalues negative for a continuous
 
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            linear system, and magnitude of eigenvalues lower than one for a
 
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            discrete-time system (as defined by <literal>syslin</literal>).
 
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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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A=diag([0.9,-2,3]);B=[0;0;1];Sl=syslin('c',A,B,[]);
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[ns,nc,U]=st_ility(Sl);
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U'*A*U
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U'*A*U
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U'*B
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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="dt_ility">dt_ility</link>
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      </member>
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      <member>
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        <link linkend="contr">contr</link>
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      </member>
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      <member>
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        <link linkend="stabil">stabil</link>
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      </member>
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      <member>
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        <link linkend="ssrand">ssrand</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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    <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="dt_ility">dt_ility</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="contr">contr</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="stabil">stabil</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="ssrand">ssrand</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
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</refentry>