ECE 497 DL Home Page

ECE 586 DL: Hybrid Systems and Control
ECE Dept, UIUC, Fall 2005

Instructor: Daniel Liberzon
Office: 144 CSL
Email: liberzon at
Phone: (217) 244-6750

Schedule: Tue Thu 1-2:20, 169 Everitt Lab.

Office hours: To be announced.

Prerequisite: ECE 515 (Linear Systems) or consent of instructor.

Text: D. Liberzon, Switching in Systems and Control, Birkhauser, 2003. Available in the bookstore.
Supplementary text: A. van der Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems, Springer, 2000.

Assignments and grading policy: Your grades will be based on homework and final project. There will be no exams in this course.


Course outline:

I. Introduction
1. Definition of a hybrid system
2. Solutions to hybrid systems
3. Examples
II. Stability analysis of hybrid systems
1. Common Lyapunov functions
2. Commutation relations and stability
3. Multiple Lyapunov functions
4. Slow switching
5. Convex combinations and state-dependent switching
III. Hybrid control design
1. Stabilization of nonholonomic systems
2. Stabilization of linear systems by hybrid feedback
3. Control with limited information
4. Switching logics and supervisory control