
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(N1)
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(NM)
 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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Lars Grüne,
Jürgen Pannek, errata last updated on 28th April 2018
