MAE 281B Nonlinear Control	Prof. M. Krstic
Homework 5	Due: May 30, 2002

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1. Extend Lemma 2.8 in Krstic et al. to systems of the form

where is continuously differentiable. Assume that and are available such that , where is a positive definite function.
Hint: Note that, by the mean-value theorem, the continuous differentiablility of implies that there exists a continuous function such that

where .

2. Apply the result from Problem 1 to stabilize the system


3. Apply the result from Problem 1 and 2 to stabilize the system


4. Compute the Sontag formula for the system from Problem 2 using the backstepping clf.

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