 ## Errata for the 2nd edition

Here you can find corrections for those errors in the second edition of the book that we are aware of:

• page 41, Problem 2(a):   the difference equation must read x(n+1) = 1/2 x(n) + sin(n+1)

• page 42, Problem 2(c):   the difference equation must read x(n+1) = (n+1)/(n+2) x(n) + sin(n+1)

• page 242, line 2:   \delta should be defined as \delta = \max_{k\in\N} \gamma_V(|x_{\mu_N}(k)|_{x^e}) + \omega(N-1)

The reason for this correction is that \nu_2 in the proof does not have the correct argument. It should read \nu_2(|x_{\mu_N}(k+1)|_{x^e}, N) everywhere, from which the specified form of \delta follows.

Note that this \delta must be bounded for the estimate (8.19) to yield a meaningful bound. This is always satisfied if the state constraint set is bounded. Otherwise, Theorem 8.33 can be used to conclude boundedness of \delta.

• page 244, line 12:   here \delta can be simplified to \delta = \omega(N-M)

• page 246, line 11:   the proof of Proposition 8.32 only works for those N>=2 for which \delta_1(N)<\Theta holds because it requires \P \subseteq Y. Hence, this inequality should be added to the assumptions of Proposition 8.32.

This is no additional restriction, since for larger N Proposition 8.32 does not yield a meaningful statement, anyway, because then Y \setminus \P is empty.

• page 247, middle: the conclusion "This inequality also shows forward invariance of Y ..." is too early at this point of the proof, because the following argument only shows x^+ \in Y for x \in Y \setminus \P. Forward invariance of Y also needs x^+ \in Y for x \in \P. This follows from the forward invariance of \P, which is shown in the remainder of the proof.

• page 248, Proof of Theorem 8.33: In the proof it should read \rho(\delta_1(...)) and \delta_1(N).

If you should discover further errors, we would appreciate a notification via email.

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© 2018 Lars Grüne, Jürgen Pannek, errata last updated on 28th April 2018