MECH/ELEC 508. Nonlinear Systems: Analysis and Control

Main Topics of the Course

  • Mathematical background and fundamental properties of nonlinear systems: Vector norms, matrix norms, matrix measures, existence and uniqueness of solutions of ordinary differential equations

  • Linearization, second order systems, periodic solutions, approximate methods

  • Lyapunov stability: Stability definitions, Lyapunov's direct method, invariance theory, stability of linear systems, Lyapunov's linearization method, converse theorems

  • Selected topics in nonlinear systems analysis and nonlinear control from

    • Input/Output stability: Small gain theorem, passivity theorem

    • Perturbation theory, averaging, and singular perturbations

    • Feedback linearization control

    • Other methods in the control of nonlinear systems such as backstepping, sliding mode and other Lyapunov-based design methods

    • Advanced nonlinear and adaptive robot control

Textbooks

  • H.K. Khalil, Nonlinear Systems (3rd Ed.), Prentice Hall

  • M. Vidyasagar, Nonlinear Systems Analysis (2nd Ed.), Prentice Hall