# Errata for the book Hybrid System Identification by F. Lauer and G. Bloch

### Notations

• Page xiv, the definition of the indicator function should be:
Indicator function, $1_A$ is 1 if the boolean expression $A$ is true and 0 otherwise

### Chapter 4

• Page 89, in Equation (4.20) the argmax should be an argmin and (4.20) should read
$$q_k \in \underset{j\in[s]}{\arg\min}\ \ell(y_k - f_j(\boldsymbol{x}_k)),\quad k=1,\dots,N.$$

### Chapter 5

• Page 107, the unnumbered Equation in the middle of the page should be written with a non-strict inequality sign as
$$\max_{k\in \mathcal{I}_1(\g \theta^*)} | y_k - \g x_k^\top \g \theta | \leq \epsilon$$
• Page 127: section 5.4 considers a cost function for switching linear regression that is the sum of squared errors instead of the mean. Therefore, Eq. (5.24) shoud be $$J(\g \theta) = \sum_{k=1}^N \min_{j\in[s]}(y_k - \g x_k^\top \g \theta_j)^2$$ instead of $$J(\g \theta) = \frac{1}{N} \sum_{k=1}^N \min_{j\in[s]}(y_k - \g x_k^\top \g \theta_j)^2$$
• Page 133, the last line of Eq. (5.43) should be $$\geq \sum_{k\in \mathcal{I}_0(B)} \left\{\left(e_k^U(B) \right)_+^2 + \left(e_k^L(B)\right)_-^2, \ \epsilon^2 \right\} + \min_{\g \theta\in B} \sum_{k\in \mathcal{I}_1(B)} e_k^2(\g \theta) + \epsilon^2 |\mathcal{I}_2(B)|$$ instead of $$\geq \sum_{k\in \mathcal{I}_0(B)}\min_{j\in[s]} \left\{\left(e_k^U(B_j) \right)_+^2 + \left(e_k^L(B_j)\right)_-^2 \right\} + \min_{\g \theta\in B} \sum_{k\in \mathcal{I}_1(B)} e_k^2(\g \theta) + \epsilon^2 |\mathcal{I}_2(B)|$$

### Appendix B

• Page 249, Section B.2.8.1, in the definition of $\boldsymbol{S}^+$, there is an extra $q$ that ought not to be there and the Eq. should read
$$\g S^+ = \begin{bmatrix} \frac{1}{\sigma_1} & 0 &\dots& 0& \dots & 0 \\ \vdots & \ddots & & \vdots & & \vdots\\ \vdots & & \frac{1}{\sigma_r} & \vdots & & \vdots\\ % \vdots & & 0 & 0 \\ 0 & \ldots & \ldots & 0 & \ldots & 0 \end{bmatrix}$$
• Page 249, Section B.2.8.2, $\tilde{U}$ should appear in bold as $\tilde{\g U}$ in the text "Indeed, since $\tilde{\g U}$ is orthogonal".