EE 8215 – Nonlinear Systems

Mihailo Jovanovic, University of Minnesota, Spring 2013

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.

Class schedule
TuTh, 2:30pm - 3:45pm, Keller Hall 3-125; Jan 22 - May 10, 2013

Instructor and Teaching Assistant

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

  • Teaching Assistant
    Xiaofan Wu
    Office: Keller Hall 2-276
    Regular office hours: Wednesday, 4:45pm - 5:45pm
    Extra office hours: Monday, 4:45pm - 5:45pm (only when HW is due Tuesday)

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 allowed. 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 26
    Final exam or Project presentation: during exam week


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


  • 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.