<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>gcare</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="gcare"> control Riccati equation</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[X,F]=gcare(Sl)  </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>X</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: symmetric matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>F</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    Generalized Control Algebraic Riccati Equation (GCARE).
    <VERB>X</VERB> = solution , <VERB>F</VERB> = gain.</P>
    <P>
    The GCARE for <VERB>Sl=[A,B,C,D]</VERB> is:</P>
    <VERBATIM>
<![CDATA[
(A-B*Si*D'*C)'*X+X*(A-B*Si*D'*C)-X*B*Si*B'*X+C'*Ri*C=0
   ]]>
    </VERBATIM>
    <P>
    where <VERB>S=(eye()+D'*D)</VERB>, <VERB>Si=inv(S)</VERB>, <VERB>R=(eye()+D*D')</VERB>, <VERB>Ri=inv(R)</VERB> 
    and <VERB>F=-Si*(D'*C+B'*X)</VERB> is such that <VERB>A+B*F</VERB> is stable.</P>
  </DESCRIPTION>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>gfare</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
