MAE 281A
Nonlinear Systems
Prof. M. Krstic
Homework 5
Due: March 12, 2002
1. Khalil, Exercise 3.41.
Hint: In part (b), study (local) u.a.s. of the solution
.
2. Khalil, Exercise 5.5.
Hint: Use completion of squares in
.
3. Khalil, Exercise 5.18, Parts (a)-(c).
Hint: In Part (c), show that stability is not
global
by showing that there exist multiple equilibria.
4. Khalil, Exercise 5.21, Parts (2) and (3).
5. Khalil, Exercise 5.22, Parts (1) and (4).
Hints:
Part (1): use Lemma C.4 in [KKK].
Part (4): use Young's inequality which gives
and
; then apply Theorem C.3 in [KKK].
.
.
.
and 
; then apply Theorem C.3 in [KKK].