EE 8215 – Nonlinear Systems

Course description

Introduction. Examples of nonlinear systems. State-space models. Equilibrium points. Linearization. Range of nonlinear phenomena: finite escape time, multiple isolated equilibria, limit cycles, chaos. Bifurcations. Phase portraits. Bendixson and Poincare-Bendixson criteria. Mathematical background: existence and uniqueness of solutions, continuous dependence on initial conditions and parameters, normed linear spaces, comparison principle, Bellman-Gronwall Lemma. Lyapunov stability. Lyapunov's direct method. Lyapunov functions. LaSalle's invariance principle. Estimating region of attraction. Center manifold theory. Stability of time-varying systems. Input-output and input-to-state stability. Small gain theorem. Passivity. Circle and Popov criteria for absolute stability. Perturbation theory and averaging. Singular perturbations. Feedback and input-output linearization. Zero dynamics. Backstepping design. Control Lyapunov functions.

TuTh, 2:30pm - 3:45pm, Keller Hall 3-115

Instructor and Teaching Assistant

• Instructor
  Mihailo Jovanovic
  Office: Keller Hall 5-157
  Office hours: Tu 3:45pm - 4:45pm (or by appointment)

• Teaching Assistant
  Sourav Pradhan
  Office: Keller Hall
  Regular office hours: Mo 4:30 - 6:30pm
  Extra office hours: Wed 4:30 - 6:30pm (when homework is due Th)

Textbook and software

• Textbook
  Hassan K. Khalil
  Nonlinear Systems
  Prentice Hall, Third Edition, ISBN 0-13-067389-7

• Software
  Homework sets will make a use of Matlab and Simulink

Grading policy

• Homework (40%)
  Midterm exam (30%)
  Final exam or Project (30%)

• Homework policy
  Homework is intended as a vehicle for learning, not as a test. Moderate collaboration with your classmates is encouraged. However, I urge you to invest enough time alone to understand each homework problem, and independently write the solutions that you turn in. Homework is generally handed out every Thursday, and it is due at the beginning of the class a week later. Late homework will not be accepted. Start early!

• Tentative exam schedule
  Midterm: Feb 25
  Final exam or Project presentation: during exam week

Prerequisites

• Even though I plan to cover everything from scratch, the students would benefit from an exposure to linear systems (EE/AEM 5231 or an equivalent course). Those interested should contact the instructor.

Acknowledgment

• I would like to thank Prof. Murat Arcak for sharing with me the material that he developed for his Nonlinear Systems Course (EE 222) at UC Berkeley.