View source for Errata: F R v F^T term dropped in proof of Theorem 7.4

{{errata page
| chapter = Output Feedback
| page = 216
| line = -7 to -3
| contributor = J. Bechhoefer
| date = 8 Mar 09
| rev = 2.10b
| version = Second printing
| text = 
In the proof of Theorem 7.4, the term <math>F R_v F^T</math> is dropped in the equations for <math>P[k+1]</math>.  The text should read:
<blockquote>
By definition,
<center><amsmath>
  \aligned 
    P[k+1] &= E\{(x[k+1] - \hat x[k+1]) (x[k+1] - \hat x[k+1])^T\} \\
    &= (A - LC) P[k] (A - LC)^T + F R_v F^T + L R_w L^T \\
    &= A P[k] A^T + F R_v F^T - A P[k] C^T L^T - L C P[k] A^T \\
    & \qquad + L (R_w + C P[k] C^T) L^T.
  \endaligned
</amsmath></center>
Letting <math>R_\epsilon = (R_w + C P[k] C^T)</math>, we have
<center><amsmath>
  \aligned 
    P[k+1] &= A P[k] A^T + F R_v F^T - A P[k] C^T L^T - L C P[k] A^T +
      L R_\epsilon L^T \\ 
    &= A P[k] A^T + F R_v F^T +
      \bigl(L \!-\! A P[k] C^T R_\epsilon^{-1} \bigr) R_\epsilon 
      \bigl(L \!-\! A P[k] C^T R_\epsilon^{-1} \bigr)^T \\
    &\qquad - A P[k] C^T R_\epsilon^{-1} C P^T[k] A^T.
  \endaligned
</amsmath></center>

</blockquote>
}}