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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) INRIA - P. Gahinet
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
*
-->
<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="linfn">
<refnamediv>
<refname>linfn</refname>
<refpurpose>infinity norm</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[x,freq]=linfn(G,PREC,RELTOL,options);</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>G</term>
<listitem>
<para>
is a <literal>syslin</literal> list
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>PREC</term>
<listitem>
<para>desired relative accuracy on the norm</para>
</listitem>
</varlistentry>
<varlistentry>
<term>RELTOL</term>
<listitem>
<para>relative threshold to decide when an eigenvalue can be considered on the imaginary axis.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>options</term>
<listitem>
<para>
available options are <literal>'trace'</literal> or <literal>'cond'</literal>
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>x</term>
<listitem>
<para>is the computed norm.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>freq</term>
<listitem>
<para>vector</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Computes the Linf (or Hinf) norm of <literal>G</literal>
This norm is well-defined as soon as the realization
<literal>G=(A,B,C,D)</literal> has no imaginary eigenvalue which is both
controllable and observable.
</para>
<para>
<literal>freq</literal> is a list of the frequencies for which <literal>||G||</literal> is
attained,i.e., such that <literal>||G (j om)|| = ||G||</literal>.
</para>
<para>
If -1 is in the list, the norm is attained at infinity.
</para>
<para>
If -2 is in the list, <literal>G</literal> is all-pass in some direction so that
<literal>||G (j omega)|| = ||G||</literal> for all frequencies omega.
</para>
<para>
The algorithm follows the paper by G. Robel
(AC-34 pp. 882-884, 1989).
The case <literal>D=0</literal> is not treated separately due to superior
accuracy of the general method when <literal>(A,B,C)</literal> is nearly
non minimal.
</para>
<para>
The <literal>'trace'</literal> option traces each bisection step, i.e., displays
the lower and upper bounds and the current test point.
</para>
<para>
The <literal>'cond'</literal> option estimates a confidence index on the computed
value and issues a warning if computations are
ill-conditioned
</para>
<para>
In the general case (<literal>A</literal> neither stable nor anti-stable),
no upper bound is prespecified.
</para>
<para>
If by contrast <literal>A</literal> is stable or anti stable, lower
and upper bounds are computed using the associated
Lyapunov solutions.
</para>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="h_norm">h_norm</link>
</member>
</simplelist>
</refsection>
</refentry>
|
