# 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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{{errata page | {{errata page | ||

− | | chapter = | + | | chapter = Dynamic Behavior |

− | | page = | + | | page = 116 |

− | | line = | + | | line = 4, 7 |

− | | contributor = | + | | 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

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Location: page 116, line 4, 7

The correct Lyapunov equations are

and

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