ECE598MAB: Geometric Control Theory

Teaching Staff

  • M.-A. Belabbas, Office: CSL 166, email:
    Assistant: Linda Stimson, CSL 153.
  • Office hours are by appointment.

Meeting times

The class meets Tuesday and Thursday 2:00pm to 3:20pm in ECEB 3017.


There will be roughly 4-5 homeworks assigned throughout the course. The homework are designed to help you verify and further your understanding of the material covered in the class, or of material not-covered.






code for HW2


  • There is no final exam, but a final project with written report (4-8 pages) and oral presentation (30 mins)


There are no mandatory textbooks. Lecture notes will be posted as we go along.


The official prerequisites for this course are ECE 515 (Control system theory and design) and ECE 528 (Nonlinear systems). In practice, a good understanding of linear algebra, multivariable calculus  and the willingness to do additional work on the way to cover possible gaps in your background should be enough. If you fall in this latter category, please discuss first with me.


Lecture notes will be posted here. They are a work in progress, so please check back for updated versions.

Chapters 0-2 (Jan 18 2018)

Chapter 0-4  (Feb 5 2018)

Ch 5 Observability 

Feedback stabilization link [Link fixed — email me if it does not work]

Feedback Linearization and Gradient flows on manifolds link

Intro to differential geometry for control pdf


The paper “Early days of geometric control”, by Brockett, is a good read on the historical development of the field. (for the published version, follow this link; you can access it if on campus or using the campus VPN)

The following books are helpful in understanding parts of the material covered.

  1. W. Boothby, Introduction to Differential Geometry and Lie Groups, Academic Press, N.Y., 1976.
  2. Frank Warner, Foundations of Differentiable Manifolds, Springer, New York, 1983.
  3. Alberto Isidori Nonlinear Control Systems: An Introduction, Second Ed. Springer,New York, 1989.
  4. R. Abraham and J. Marsden, Foundations of Mechanics (Second Ed.) Addison- Wesley, Reading, Mass., 1979.
  5. V.I. Arnold, Mathematical Methods in Classical Mechanics, Springer-Verlag New York, 1989.
  6. Velimir Jurdjevic, Geometric Control Theory, Cambridge University Press, Cam- bridge, England, 1997.
  7. Anthony Bloch, Nonholonomic Mechanics and Control, Springer-Verlag NY, 2003
  8. R.W. Brockett, Finite Dimensional Linear Systems, J. Wiley, N.Y., 1970.
  9. Francesco Bullo and Andrew D. Lewis, Geometric Control of Mechanical Systems, Springer-Verlag,  2004