# CDS 240, Spring 2016: HW 2

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R. Murray, J. Doyle | Issued: 17 Apr 2016 (Sun) |

CDS 240, Spring 2016 | Due: 25 Apr 2016 (Mon) |

- Khalil, Problem 5.1
- Khalil, Problem 5.16
- Hint: Try using the Lyapunov function $$V(x) = \int_0^{x_1} \sigma(y) dy + \frac{1}{2} (x_1^2 + x_2^2)$$.

- Khalil, Problem 5.23
- Khalil, Problem 6.2
- Khalil, Problem 6.6
- Khalil, Problem 6.7
- Khalil, Problem 7.3
- Khalil, Problem 7.6
- Hint: See Example 7.4 to see how to estimate the region of attraction in part (c)

- Khalil, Problem 7.10, nonlinearities (3) and (4)
- Khalil, Problem 7.14, parts (a) and (c)