Lecture notes from Spring 2015 (courtesy of James Schmidt; 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: TBA (no homework questions, please)
Homework TA: Ivan Abraham
Email: itabrah2 at illinois.edu
Office hours: TBA
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, during the week of Mar 5) - 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.