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  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

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man/eng/robust/rowinout.xml
 
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<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
 
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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
 
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<MAN>
 
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  <LANGUAGE>eng</LANGUAGE>
 
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  <TITLE>rowinout</TITLE>
 
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  <TYPE>Scilab Function</TYPE>
 
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  <DATE>April 1993</DATE>
 
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  <SHORT_DESCRIPTION name="rowinout"> inner-outer factorization</SHORT_DESCRIPTION>
 
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  <CALLING_SEQUENCE>
 
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    <CALLING_SEQUENCE_ITEM>[Inn,X,Gbar]=rowinout(G)  </CALLING_SEQUENCE_ITEM>
 
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  </CALLING_SEQUENCE>
 
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  <PARAM>
 
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    <PARAM_INDENT>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>G</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: linear system (<VERB>syslin</VERB> list) <VERB>[A,B,C,D]</VERB></SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>Inn</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>:  inner factor (<VERB>syslin</VERB> list)</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>Gbar</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>:  outer factor (<VERB>syslin</VERB> list)</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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      <PARAM_ITEM>
 
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        <PARAM_NAME>X</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>:  row-compressor of <VERB>G</VERB> (<VERB>syslin</VERB> list)</SP>
 
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        </PARAM_DESCRIPTION>
 
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      </PARAM_ITEM>
 
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    </PARAM_INDENT>
 
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  </PARAM>
 
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  <DESCRIPTION>
 
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    <P>
 
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    Inner-outer factorization (and row compression) of (<VERB>l</VERB>x<VERB>p</VERB>) <VERB>G =[A,B,C,D]</VERB> with <VERB>l&gt;=p</VERB>.</P>
 
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    <P><VERB>G</VERB> is assumed to be tall (<VERB>l&gt;=p</VERB>) without zero on the imaginary axis
 
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    and with a <VERB>D</VERB> matrix which is full column rank.</P>
 
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    <P><VERB>G</VERB> must also be stable for having <VERB>Gbar</VERB> stable.</P>
 
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    <P><VERB>G</VERB> admits the following inner-outer factorization:</P>
 
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    <VERBATIM>
 
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<![CDATA[
 
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         G = [ Inn ] | Gbar |
 
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                     |  0   |
 
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   ]]>
 
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    </VERBATIM>
 
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    <P>
 
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    where <VERB>Inn</VERB> is square and inner (all pass and stable) and <VERB>Gbar</VERB> 
 
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    square and outer i.e:
 
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    Gbar is square bi-proper and bi-stable (Gbar inverse is also proper 
 
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    and stable);</P>
 
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    <P>
 
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    Note that:</P>
 
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    <VERBATIM>
 
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<![CDATA[
 
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         [ Gbar ]
 
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   X*G = [  -   ]
 
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         [  0   ]
 
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   ]]>
 
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    </VERBATIM>
 
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    <P>
 
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    is a row compression of <VERB>G</VERB> where <VERB>X</VERB> = <VERB>Inn</VERB> inverse is all-pass i.e:</P>
 
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    <VERBATIM>
 
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<![CDATA[
 
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 T
 
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X (-s) X(s) = Identity
 
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   ]]>
 
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    </VERBATIM>
 
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    <P>
 
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    (for the continous time case).</P>
 
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  </DESCRIPTION>
 
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  <SEE_ALSO>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>syslin</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>colinout</LINK>
 
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    </SEE_ALSO_ITEM>
 
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  </SEE_ALSO>
 
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</MAN>