EE 587 – Nonlinear Control Systems

Mihailo Jovanovic, University of Southern California, Spring 2023

Target audience

Graduate students with interests in control and dynamical systems, robotics, artificial intelligence and machine learning, signal and image processing, communications, computer science and engineering, optimization, power systems, systems biology, and financial engineering.

Course description

Introduction and 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. Control Lyapunov functions. Center manifold theory. Stability of time-varying systems. Gradient algorithm for estimation of unknown parameters. Uniform observability and persistency of excitation. Input-output and input-to-state stability. Small gain theorem. Positive real transfer functions. Kalman-Yakubovich-Popov Lemma. Passivity. Circle and Popov criteria for absolute stability. Theory of integral quadratic constraints. Feedback and input-output linearization. Relative degree and zero dynamics. Model reference adaptive control. Integrator backstepping. Adaptive backstepping design.

Class schedule
Mo/Wed, 10:00 - 11:50am, Dr. Joseph Medicine Crow Center for International and Public Affairs (CPA) 155

Instructor and Teaching Assistant

  • Instructor
    Mihailo Jovanovic
    Office: EEB 344
    Office hours: Wed 12:00pm - 1:00pm (or by appointment)

  • Teaching Assistant
    Office: TBD
    Office hours: TBD

Text and software

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

  • Software
    Homework sets will make a use of Matlab or 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 other 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: March 8
    Final exam or Project presentation: during exam week


  • Even though I plan to cover everything from scratch, the students would benefit from an exposure to linear systems (EE 585 or an equivalent course). Those interested should contact the instructor.