ECE 497 DL Home Page

ECE 497 DL: Hybrid Systems and Control
ECE Dept, UIUC, Fall 2002

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

Schedule: Mon Wed 12:30-1:50, 170 Everitt Lab.

Office hours: Tue 11:30-1, Fri 3:30-5.

Prerequisite: ECE 415 (Linear Systems) or consent of instructor.

Text: Lecture notes by the instructor. Available for purchase in 61 Everitt Lab.
Supplementary text: A. van der Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems, Springer, 2000. A copy has been placed on reserve in Grainger library.

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


MATLAB files for the nonholonomic robot simulation: sfrobota.m, robotmpg.m,

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