Errata: Example 8.10 missing factor of v, a1 and a2 flipped

Chapter	Output Feedback
Page	8-28
Line	-4
Version	3.1.5
Date	6 Oct 2021

Example 8.10 (Steering control with velocity scheduling) is missing a factor of $v$ in the definition of $A_{\text{d}}$ that propagates through the example. In addition, the coefficients $a_{1}$ and $a_{2}$ are swapped in the definition of $w_{2}$.

The equation for $A_{\text{d}}$ should read:

$A_{\text{d}}=\left.{\frac {\partial f}{\partial x}}\right|_{(x_{\text{d}},u_{\text{d}})}=\left.{\begin{bmatrix}0&0&-{\color {blue}v}\sin \theta \\0&0&{\color {blue}v}\cos \theta \\0&0&0\end{bmatrix}}\right|_{(x_{\text{d}},u_{\text{d}})}={\begin{bmatrix}0&0&0\\0&0&v_{\text{r}}\\0&0&0\end{bmatrix}},$

This leads to an error in the definition of $w_{2}$ later in the example. In addition, the coefficients $a_{1}$ and $a_{2}$ are swapped, so the definition of $w_{2}$ should be:

$w_{2}=-{\frac {l}{v_{\text{r}}}}({\frac {a_{2}}{v_{\text{r}}}}e_{y}+a_{1}e_{\theta }).$

The final controller then becomes

Failed to parse (unknown function "\begin{bmatrix}"): {\displaystyle \begin{bmatrix} v \\ \phi \end{bmatrix} = -\underbrace{\begin{bmatrix} \lambda_1 & 0 & 0 \\ 0 & \dfrac{a_2 l}{v_\text{r}^2} & \dfrac{a_1 l}{v_\text{r} \end{bmatrix} }_{K_\text{d}} \underbrace{\begin{bmatrix} x - v_\text{r} t \\ y - y_\text{r} \\ \theta} \end{bmatrix}_{e} + \underbrace{\begin{bmatrix} v_\text{r} \\ 0}\vphantom{\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}} \end{bmatrix}_{u_\text{d}}. }