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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>arhnk</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="arhnk"> Hankel norm approximant</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[slm]=arhnk(sl,ord,[tol])     </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>sl</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: linear system (<VERB>syslin</VERB> list)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>ord</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: integer, order of the approximant</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>tol</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: threshold for rank determination in <VERB>equil1</VERB></SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    computes <VERB>slm</VERB>, the optimal Hankel norm approximant of the 
    stable continuous-time linear system <VERB>sl</VERB> with matrices <VERB>[A,B,C,D]</VERB>.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
A=diag([-1,-2,-3,-4,-5]);B=rand(5,1);C=rand(1,5);
sl=syslin('c',A,B,C);
slapprox=arhnk(sl,2);
[nk,W]=hankelsv(sl);nk
[nkred,Wred]=hankelsv(slapprox);nkred
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>equil</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>equil1</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>hankelsv</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
