Homework 1 (posted Jan 29, due Feb 10) | Solution (posted Feb 23)
Homework 2 (posted Feb 19, due Mar 3) | Solution (posted Mar 17)
Homework 3 (posted Mar 19, due Apr 7) | Solution (posted Apr 23)
Homework 4 (posted Apr 9, due Apr 21) | Solution (posted Apr 30)
Lecture notes (courtesy of James Schmidt)
Schedule: Tue Thu 11:00-12:20, 3015 ECE Building.
Prerequisites: ECE 515 (Linear Systems) and Math 285 or 441 (Differential Equations).
Instructor: Daniel Liberzon
Office: 144 CSL
Email: liberzon at illinois.edu
Office hours: Fri 11:00-12:30 unless posted otherwise (no homework questions, please)
Homework TA: Guosong (Oliver) Yang
Email: yang150 at illinois.edu
Office hours: Mon 2:30-4:00pm in 368 CSL
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) - 50% of the grade, final exam - 50%.
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.