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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>abcd</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="feedback"> feedback operation</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>Sl=Sl1/.Sl2</CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>Sl1,Sl2</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: linear systems (<VERB>syslin</VERB> list) in state-space or transfer form, or ordinary gain matrices.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>Sl</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: linear system (<VERB>syslin</VERB> list) in state-space or transfer form</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    The feedback operation is denoted by <VERB> /. </VERB> (slashdot).
    This command returns <VERB>Sl=Sl1*(I+Sl2*Sl1)^-1</VERB>, i.e the (negative) 
    feedback of <VERB>Sl1</VERB> and <VERB>Sl2</VERB>. <VERB>Sl</VERB> is the transfer
    <VERB> v -&gt; y</VERB> for <VERB> y = Sl1 u</VERB>, <VERB>u = v - Sl2 y</VERB>.</P>
    <P>
    The result is the same as <VERB>Sl=LFT([0,I;I,-Sl2],Sl1)</VERB>.</P>
    <P>
    Caution: do not use with decimal point (e.g. <VERB>1/.1</VERB> is ambiguous!)</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
S1=ssrand(2,2,3);S2=ssrand(2,2,2);
W=S1/.S2;
ss2tf(S1/.S2)
//Same operation by LFT:
ss2tf(lft([zeros(2,2),eye(2,2);eye(2,2),-S2],S1))
//Other approach: with constant feedback
BigS=sysdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
Bigclosed=BigS/.F;
W1=Bigclosed(1:2,1:2);   //W1=W (in state-space).
ss2tf(W1)
//Inverting
ss2tf(S1*inv(eye()+S2*S1))
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>lft</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>sysdiag</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>augment</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>obscont</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
