Homework 1 (posted Jan 29, due Feb 10) | Homework 2 (posted Feb 19, due Mar 3) | Homework 3 (posted Mar 17, due Apr 2) | Homework 4 (posted Apr 9, due Apr 23)
Schedule: Tue Thu 10:00-11:20, 300 Noyes Lab.
Prerequisites: ECE 515 (Linear Systems) and Math 285 or 441 (Differential Equations).
Instructor: Daniel Liberzon
Office: 144 CSL
Email: liberzon at uiuc.edu
Office hours (subject to change): Tuesdays 4-5:30. Exception: when HW is due on Tuesday, office hours will be moved to Monday 4-5:30.
H. K. Khalil, Nonlinear Systems, 3rd edition. Prentice Hall,
Supplementary text: E. D. Sontag, Mathematical Control Theory, 2nd edition. Springer, 1998. Available from the author's website.
Assignments and grading policy: Homework (4-5 problem sets) - 40% of the grade, final exam (take-home) - 60%.
Brief course outline:
1. Mathematical background.
2. Fundamental properties of dynamical systems: existence and uniqueness of solutions, continuous dependence on initial conditions and parameters, comparison principles.
3. Stability analysis: Lyapunov stability of autonomous and nonautonomous systems, LaSalle's invariance principle, converse Lyapunov theorems, stability of feedback systems, effects of perturbations.
4. Systems with inputs and outputs: input-to-state stability and related notions, Lyapunov characterizations.
5. Nonlinear control: control Lyapunov functions, universal formulas for feedback stabilization and disturbance attenuation.
6. Advanced topics (time permitting): center manifold theorem, averaging, singular perturbations.