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:

Failed to parse (syntax error): {\displaystyle 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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{bmatrix} v \\ \phi} = -\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{\bmat{0 \\ 0 \\ 0}}\end{bmatrix}_{u_\text{d}}. }