ECE1648S - Nonlinear Control Systems

Last modified January 17, 2017


M. Maggiore GB437 maggiore (at)


Course starts on January 16

Day and Time Room
Mon 1-2:30


Wed 1-2:30 BA B025

Course Outline

The concepts and techniques presented in this course will be complemented by control design examples for synchronization, path following, and coordination.

  • Introduction to differentiable manifolds
  • The feedback equivalence problem
    • Feedback linearization
    • Stabilization and tracking for feedback linearizable systems
    • Application to robotics
  • Invariant and controlled invariant manifolds; the zero dynamics algorithm
    • Application to a synchronization problem
    • Application to virtual holonomic constraints for mechanical systems
  • Invariant distributions and quotient systems


There will be five homework assignments(40%), a final project (40%), and a final presentation (20%). I will post a list of projects on the Blackboard website. The list will give you some ideas, and you can use it as a starting point to formulate a project proposal subject to my approval. You will produce a project report and will present your finding to the entire class at the end of the course. My evaluation of your project will be based on your document and your presentation.


  • Differential geometry
    • J. M. Lee: Introduction to Smooth Manifolds, Springer, 2003

    See also:

    • V.I. Arnold: Ordinary Differential Equations, MIT Press, 1978
    • M. Spivak: A Comprehensive Introduction to Differential Geometry, vol. 1, Third Ed., Publish or Perish, 2005
    • V. Guillemin, A. Pollack: Differential Topology, Prentice Hall, 1974
    • W. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed., Academic Press, 1986


  • Geometric nonlinear control
    • Alberto Isidori: Nonlinear Control Systems, Third Edition, Springer Verlag, 1995

    See also:

    • H. Nijmeijer, A.J. van der Schaft: Nonlinear Dynamical Systems, Springer Verlag, 1990
    • V. Jurdjevic: Geometric Control Theory, Cambridge University Press, 1996
    • A. Agrachev, Y. Sachkov: Control Theory from the Geometric Viewpoint, Springer, 2004


  • A comprehensive reference on nonlinear control systems
    • Hassan Khalil: Nonlinear Systems, Third Edition, Prentice Hall, 2002