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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>h_cl</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="h_cl"> closed loop matrix</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[Acl]=h_cl(P,r,K)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[Acl]=h_cl(P22,K)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>P, P22</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: linear system (<VERB>syslin</VERB> list), augmented plant or nominal plant respectively</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>r</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: 1x2 row vector, dimensions of 2,2 part of <VERB>P</VERB> (<VERB>r=[rows,cols]=size(P22)</VERB>)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>K</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: linear system (<VERB>syslin</VERB> list), controller</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>Acl</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real square matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    Given the standard plant <VERB>P</VERB> (with <VERB>r=size(P22)</VERB>) and the controller
    <VERB>K</VERB>, this function returns the closed loop matrix <VERB>Acl</VERB>.</P>
    <P>
    The poles of <VERB>Acl</VERB> must be stable for the internal stability 
    of the closed loop system.</P>
    <P><VERB>Acl</VERB> is the <VERB>A</VERB>-matrix of the linear system <VERB>[I -P22;-K I]^-1</VERB> i.e.
    the <VERB>A</VERB>-matrix of <VERB>lft(P,r,K)</VERB></P>
  </DESCRIPTION>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>lft</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
  <AUTHOR>F. D.  </AUTHOR>
</MAN>
