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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/control/lin.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>lin</TITLE>
 
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  <TYPE>Scilab Function</TYPE>
 
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  <DATE>April 1993</DATE>
 
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  <SHORT_DESCRIPTION name="lin"> linearization</SHORT_DESCRIPTION>
 
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  <CALLING_SEQUENCE>
 
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    <CALLING_SEQUENCE_ITEM>[A,B,C,D]=lin(sim,x0,u0)  </CALLING_SEQUENCE_ITEM>
 
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    <CALLING_SEQUENCE_ITEM>[sl]=lin(sim,x0,u0)  </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>sim</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: function</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>x0, u0</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: vectors of compatible dimensions</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>A,B,C,D</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: real matrices</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>sl</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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          <SP>: <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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    linearization of the non-linear system <VERB>[y,xdot]=sim(x,u)</VERB>
 
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    around <VERB>x0,u0</VERB>.</P>
 
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    <P><VERB>sim</VERB> is a function which computes <VERB>y</VERB> and <VERB>xdot</VERB>.</P>
 
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    <P>
 
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    The output is a linear system (<VERB>syslin</VERB> list) <VERB>sl</VERB> or the 
 
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    four matrices <VERB>(A,B,C,D)</VERB></P>
 
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    <P>
 
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    For example, if <VERB>ftz</VERB> is the function passed to ode e.g.</P>
 
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    <VERBATIM>
 
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<![CDATA[
 
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[zd]=ftz(t,z,u)
 
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   ]]>
 
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    </VERBATIM>
 
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    <P>
 
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    and if we assume that <VERB>y=x</VERB></P>
 
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    <P><VERB>[z]=ode(x0,t0,tf,list(ftz,u)</VERB> compute <VERB>x(tf)</VERB>.</P>
 
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    <P>
 
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    If <VERB>simula</VERB> is the following function:</P>
 
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    <VERBATIM>
 
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<![CDATA[
 
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deff('[y,xd]=simula(x,u)','xd=ftz(tf,x,u); y=x;');
 
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   ]]>
 
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    </VERBATIM>
 
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    <P>
 
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    the tangent linear system <VERB>sl</VERB> can be obtained by:</P>
 
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    <VERBATIM>
 
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<![CDATA[
 
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[A,B,C,D]=lin(simula,z,u)
 
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sl = syslin('c',A,B,C,D,x0)
 
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   ]]>
 
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    </VERBATIM>
 
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  </DESCRIPTION>
 
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  <EXAMPLE>
 
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<![CDATA[
 
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deff('[y,xdot]=sim(x,u)','xdot=[u*sin(x);-u*x^2];y=xdot(1)+xdot(2)')
 
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sl=lin(sim,1,2);
 
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 ]]>
 
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  </EXAMPLE>
 
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  <SEE_ALSO>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>external</LINK>
 
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    </SEE_ALSO_ITEM>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>derivat</LINK>
 
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    </SEE_ALSO_ITEM>
 
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  </SEE_ALSO>
 
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</MAN>