# Difference between revisions of "CDS 140b Spring 2014 Homework 4"

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 R. Murray, D. MacMartin Issued: 30 Apr 2014 (Wed) CDS 140b, Spring 2014 Due: 8 May 2014 (Thu)

__MATHJAX__

1. Khalil, Problem 9.2
2. Khalil, Problem 9.3
3. Khalil, Problem 9.6
4. Khalil, Problem 9.17
5. Khalil, Problem 9.29
• For part b, let $\|\dot r(t)\| \leq \epsilon$, for all $t \geq 0$. Reason why there exists a Lyapanov function satisfying equations (9.41)-(9.44). Then explain why for some sufficiently small epsilon, solutions are uniformly ultimately bounded to a ball bound the equilibrium point $(\bar x, \bar z)$, with a radius of the ball in proportion to $\epsilon$, and that therefore the norm of the tracking error is smaller than $k \epsilon$ for some $k>0$. Also, what happens to the tracking error when $\dot r(t) \to 0$ as $t \to \infty$?