MAE 281B
Nonlinear Control 		Prof. M. Krstic

Homework 6 		Due: June 6, 2002


1. Consider the system

Given a smooth known reference signal , design a control law that achieves asymptotic tracking, i.e. , while keeping bounded.
Hint: Consider the system as a block-strict-fbk form with as the first block. Start the backstepping procedure with .

2. Design a (robust) controller based on nonlinear damping and backstepping which achieves input-to-state stability with respect to the perturbation in the system
Can you derive a linear controller that globally asymptotically stabilizes the equilibrium in the case where is constant and nonpositive?

3. Design a controller that achieves noise-to-state stability for the stochastic system
where is an independent Wiener process with .

4. Design an output-feedback controller that achieves global asymptotic stability of the equilibrium at the origin of the system