CDS 240, Spring 2016: HW 2

R. Murray, J. Doyle	Issued: 17 Apr 2016 (Sun)
CDS 240, Spring 2016	Due: 25 Apr 2016 (Mon)

1. Khalil, Problem 5.1
2. Khalil, Problem 5.16
   • Hint: Try using the Lyapunov function $$V(x) = \int_0^{x_1} \sigma(y) dy + \frac{1}{2} (x_1^2 + x_2^2)$$.
3. Khalil, Problem 5.23
4. Khalil, Problem 6.2
5. Khalil, Problem 6.6
6. Khalil, Problem 6.7
7. Khalil, Problem 7.3
8. Khalil, Problem 7.6
   • Hint: See Example 7.4 to see how to estimate the region of attraction in part (c)
9. Khalil, Problem 7.10, nonlinearities (3) and (4)
10. Khalil, Problem 7.14, parts (a) and (c)