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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>des2tf</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="des2tf"> descriptor to transfer function conversion</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[S]=des2tf(sl)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[Bfs,Bis,chis]=des2tf(sl)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>sl</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: list (linear system in descriptor form)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>Bfs, Bis</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: two polynomial matrices</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>chis</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: polynomial</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>S</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: rational matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    Given the linear system in descriptor form i.e.
    <VERB>Sl=list('des',A,B,C,D,E)</VERB>, <VERB>des2tf</VERB> converts <VERB>sl</VERB> into
    its transfer function representation:</P>
    <VERBATIM>
<![CDATA[
S=C*(s*E-A)^(-1)*B+D
   ]]>
    </VERBATIM>
    <P>
    Called with 3 outputs arguments <VERB>des2tf</VERB> returns
    <VERB>Bfs</VERB> and <VERB>Bis</VERB> two polynomial matrices, and <VERB>chis</VERB>
    polynomial such that:</P>
    <VERBATIM>
<![CDATA[
S=Bfs/chis - Bis
   ]]>
    </VERBATIM>
    <P><VERB>chis</VERB> is the determinant of <VERB>(s*E-A)</VERB> (up to a xcative constant);</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
s=poly(0,'s');
G=[1/(s+1),s;1+s^2,3*s^3];
Descrip=tf2des(G);Tf1=des2tf(Descrip)
Descrip2=tf2des(G,"withD");Tf2=des2tf(Descrip2)
[A,B,C,D,E]=Descrip2(2:6);Tf3=C*inv(s*E-A)*B+D
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>glever</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>pol2des</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>tf2des</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>ss2tf</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>des2ss</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>rowshuff</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
  <AUTHOR>F. D.  </AUTHOR>
</MAN>
