ECE1647 - Introduction to Nonlinear Control Systems

Last modified 9/25/09.

Instructor
M. Maggiore GB437 maggiore (at) control.utoronto.ca

Lectures (course starts Sept 15, 2009)
Day and Time Room
Tue 10-12 HA401
Thu 13-15 HA316

Course Outline
  • CHAPTER 1: Mathematical preliminaries
  • CHAPTER 2: Introduction to Dynamics
    • Finite dimensional phase flows and vector fields
    • Existence and uniqueness of solutions of ODEs
    • Invariant sets and limit sets
    • The Poincare'-Bendixon theorem
    • Stability of periodic attractors
    • Centre, stable, and unstable manifolds; the stable manifold theorem
    • Elements of structural stability
  • CHAPTER 3: Stability theory
    • Stability definitions
    • Direct Lyapunov theorems for autonomous systems
    • LaSalle's invariance principle for autonomous systems
    • Massera and Kurzweil's converse Lyapunov theorems
  • CHAPTER 4: Introduction to nonlinear stabilization
    • Control Lyapunov functions
    • Artstein-Sontag Theorem
    • Brockett's necessary conditions
    • Passive systems and passivity-based stabilization

Course Notes
You'll be able to download the course notes from the Course Documents section in the University of Toronto webportal here. The notes are self-contained and serve as a textbook for this course.

Reference Texts
If the course notes are not sufficient, you may consider consulting these references:
  • V.I. Arnold, Ordinary Differential Equations, MIT Press, 1973.
  • J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Springer-Verlag, 1983.
  • J.K. Hale, Ordinary Differential Equations, Robert E. Krieger Publishing Company, 1980.
  • P. Hartman, Ordinary Differential Equations, Second edition, SIAM, 2002.
  • M.W. Hirsch, S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, 1974.
  • Hassan Khalil, Nonlinear Systems, Third Edition, Prentice Hall, 2002.