<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>balreal</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="balreal"> balanced realization</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[slb [,U] ] = balreal(sl)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>sl,slb</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: linear systems (<VERB>syslin</VERB> lists)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    Balanced realization of linear system <VERB>sl=[A,B,C,D]</VERB>. <VERB>sl</VERB>
    can be a continuous-time or discrete-time state-space system. 
    sl is assumed stable.</P>
    <VERBATIM>
<![CDATA[
slb=[inv(U)*A*U ,inv(U)*B , C*U , D]
   ]]>
    </VERBATIM>
    <P>
    is the balanced realization.</P>
    <P><VERB>slb</VERB> is returned as a <VERB>syslin</VERB> list.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
A=diag([-1,-2,-3,-4,-5]);B=rand(5,2);C=rand(1,5);
sl=syslin('c',A,B,C);
[slb,U]=balreal(sl);
Wc=clean(ctr_gram(slb))
W0=clean(obs_gram(slb))
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>ctr_gram</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>obs_gram</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>hankelsv</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>equil</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>equil1</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
