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