Homework 1 (posted Jan 29, due Feb 8) | Solution (posted Feb 19)
Homework 2 (posted Feb 19, due Mar 1) | Solution (posted Mar 12)
Homework 3 (posted Mar 23, due Apr 5) | Solution (posted Apr 11)
Homework 4 (posted Apr 9, due Apr 19) | Solution (posted Apr 30)
Lecture notes typeset by students (created by James Schmidt in Spring 2015, updated by Adriano Lima Abrantes in Spring 2018; I have not checked the notes and cannot guarantee their correctness)
Schedule: Tue Thu 11:00-12:20, 2015 ECE Building.
Prerequisites: ECE 515 (Linear Systems) and Math 444 or 447 (Real Analysis).
Instructor: Daniel Liberzon
Office: 144 CSL
Email: liberzon at illinois.edu
Office hours: please see me after class
Homework TA: Ivan Abraham
Email: itabrah2 at illinois.edu
Office hours: Tue 7:00-8:00pm in ECEB 3034. (If you can't make this time, Ivan will also be available Tue 4:00-5:00pm in CSL 164.)
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) - 30% of the grade, midterm exam (in class, Thu Mar 8) - 30%, final exam (take-home, during the week of May 7) - 40%. Note: this information is tentative and subject to change.
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.