EECI 2015 M22 Home Page

EECI M22: Switched Systems and Control (Spring 2015)

Instructor: Daniel Liberzon, University of Illinois at Urbana-Champaign, U.S.A., email: liberzon at

Location: Supélec, Gif-sur-Yvette, France, May 25-29

Switched/hybrid systems are dynamical systems that combine continuous dynamics and discrete events. Such systems are of theoretical interest and important in many applications, and have they have attracted considerable attention in the recent control literature. This graduate-level course will introduce the students to recent research results on analysis and design of switched and hybrid systems.

Course summary

Schedule and outline

Textbook and lecture notes

The course is mainly based on the following textbook:

D. Liberzon, Switching in Systems and Control, Birkhauser, 2003.

The textbook material will be supplemented by recent research articles. Also, below is a condensed set of lecture notes extracted from the textbook, which covers some of the relevant material.

Lecture notes


A tentative course syllabus is given below. Powerpoint slides for each lecture are preliminary versions and will be updated during the course. All section and page numbers in the "reading" column refer to the above textbook; some of the same material (in condensed form) can also be found in the lecture notes posted above.

TopicSlides ReadingNotes
Hybrid and switched systems and their solutionsintro.ppsxSections 1.1, 1.2  
Stability: definitions and background results noneAppendix A 
Stability under arbitrary switching and common Lyapunov functionsGUAS.ppsxSections 2.1.1-2.1.5 
Commutation relations and stability of switched systems LA.ppsxSection 2.2, Appendix B, paper 1, paper 2 
Systems with special structurestructure.ppsxSection 2.3 
Common weak Lyapunov functions; observabilityobservability.ppsxDownload paper 
Multiple Lyapunov functions and dwell-time switchingconstrained.ppsxSections 3.1, 3.2, paper
Average dwell time; multiple weak Lyapunov functions
State-dependent switchingSections 3.3, 3.4 
Input-to-state stability of switched systemsISS-invertibility.ppsx Download paper
Invertibility of switched systemsDownload paper 
Gradient algorithms; introduction to hybrid controlgradient.ppsxPaper 1, paper 2
Hybrid control of nonholonomic systemsparking.ppsxChapter 4 
Control with limited informationlimited-info.ppsxSection 5.3, paper 1, paper 2  
Switching adaptive controlsupervisory.ppsxChapter 6