Difference between revisions of "Errata: In Example 4.11, Lyapunov equation entries for f' 1 and f' 2 are switched (solution is correct)"

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(Created page with '{{subst:errata template}}')
 
 
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{{errata page
 
{{errata page
| chapter =  
+
| chapter = Dynamic Behavior
| page =  
+
| page = 116
| line =  
+
| line = 4, 7
| contributor = R. M. Murray
+
| contributor = J.-J. Jung (SNU)
| date =  
+
| date = 7 Dec 2010
 
| rev = 2.10d
 
| rev = 2.10d
 
| version = Third printing
 
| version = Third printing
 
| text =  
 
| text =  
 +
The correct Lyapunov equations are
 +
<center><amsmath>
 +
  \begin{bmatrix} -1 & {\color{blue} f'_1} \\ {\color{blue} f'_2} & -1 \end{bmatrix}
 +
  \begin{bmatrix} p_{11} & p_{12} \\ p_{12} & p_{22} \end{bmatrix} +
 +
  \begin{bmatrix} p_{11} & p_{12} \\ p_{12} & p_{22} \end{bmatrix}
 +
  \begin{bmatrix} -1 & {\color{blue} f_2'} \\ {\color{blue} f'_1} & -1 \end{bmatrix} =
 +
  \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix},
 +
</amsmath></center>
 +
and
 +
<center><amsmath>
 +
  \begin{bmatrix}
 +
    -2 p_{11} + 2 {\color{blue} f'_1} p_{12} & p_{11} {\color{blue} f'_2} - 2 p_{12} + p_{22} {\color{blue} f'_1} \\
 +
    p_{11} {\color{blue} f'_2} - 2 p_{12} + p_{22} {\color{blue} f'_1} & -2 p_{22} + 2 {\color{blue} f'_2} p_{12}
 +
  \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix},
 +
</amsmath></center>
 
}}
 
}}

Latest revision as of 18:19, 29 August 2011

Return to Errata page

Location: page 116, line 4, 7

The correct Lyapunov equations are

math

and

math

(Contributed by J.-J. Jung (SNU), 7 Dec 2010)