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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>UNOBS</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="unobs"> unobservable subspace</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[n,[U]]=unobs(A,C,[tol])   </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>A, C</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real matrices</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>tol</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: tolerance used when evaluating ranks (QR factorizations).</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>n</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: dimension of unobservable subspace.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>U</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: orthogonal change of basis which puts <VERB>(A,B)</VERB> in canonical form.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P><VERB>[n,[U]]=unobs(A,C,[tol])</VERB> gives the unobservable form of an <VERB>(A,C)</VERB> 
    pair.
    The <VERB>n</VERB> first columns of <VERB>U</VERB> make a basis for the unobservable
    subspace.</P>
    <P>
    The <VERB>(2,1)</VERB> block (made of last <VERB>nx-n</VERB> rows and <VERB>n</VERB> first 
    columns) of <VERB>U'*A*U</VERB> is zero and and the <VERB>n</VERB> first columns 
    of <VERB>C*U</VERB> are zero.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
A=diag([1,2,3]);C=[1,0,0];
unobs(A,C)
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>contr</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>contrss</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>canon</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>cont_mat</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>spantwo</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>dt_ility</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
