MAE 281B
Nonlinear Control
Prof. M. Krstic
Homework 2
Due: May 9, 2002
1. Without using a Lyapunov function
, show that the system
.
is g.a.s. for both a=1/2 and a=-1/2. Hint: for a=1/2, use the nonlinear small gain theorem; and for a=-1/2, use the passivity theorem.
2. Solve the above problem by constructing Lyapunov functions
.
3. Khalil, Exercise 10.22.
4. Khalil, Exercise 10.30.
5. Khalil, Exercise 10.32.
.
, show that the system
..