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ECE 586 DL: Hybrid Systems and Control (Fall 2009)

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 advanced graduate-level course will introduce the students to recent research results on analysis and design of switched and hybrid systems.


Instructor: Daniel Liberzon. Office: 144 CSL. Email: liberzon at
Schedule: Tue Thu 2-3:20, 57 Everitt Lab.
Office hours: Thu 3:40-5.
Prerequisite: The course will build on a standard first-year graduate course in state-space linear systems, such as ECE 515.
Some knowledge of nonlinear system analysis techniques (such as those covered in ECE 517 or ECE 528) is a plus but not a requirement.
Required text: D. Liberzon, Switching in Systems and Control, Birkhauser, 2003. Available in UofI bookstore or on
The textbook material will be supplemented by recent research articles.
Final project: This course will involve a final research project, on a topic of your choosing, with an oral presentation towards the end of the semester. There will be no exams.


A tentative course syllabus is given below. Powerpoint slides for each lecture will usually be added on the day of the lecture. To view them, it is best to save them first and then open with Powerpoint. All section and page numbers in the "reading" column refer to the textbook unless otherwise noted.

Date TopicSlides ReadingNotes
Tue Aug 25   no class (DL out of town)
Thu Aug 27   no class (DL out of town)
Tue Sep 1Hybrid and switched systems
and their solutions
intro.ppsSection 1.1  
Thu Sep 3noneSection 1.2 
Tue Sep 8Stability: definitions and
background results
noneAppendix A 
Thu Sep 10noneAppendix A 
Tue Sep 15Stability under arbitrary switching and
common Lyapunov functions
GUAS.ppsSections 2.1.1-2.1.3 
Thu Sep 17noneSections 2.1.4, 2.1.5 
Tue Sep 22Commutation relations and
stability of switched systems
LA.ppsSection 2.2, Appendix B 
Thu Sep 24Paper 1, paper 2 
Tue Sep 29Systems with special structurestructure.ppsSection 2.3 
Thu Oct 1   no class: Allerton conference
Tue Oct 6Common weak Lyapunov functions; observabilityobservability.ppsDownload paper 
Thu Oct 8Multiple Lyapunov functions and dwell-time switchingconstrained.ppsSections 3.1, 3.2, paper  
Tue Oct 13Average dwell time; multiple weak Lyapunov functionswill finish at 2:50pm (CSL seminar)
Thu Oct 15State-dependent switchingSections 3.3, 3.4 
Tue Oct 20Input-to-state stability of switched systemsISS-invertibility.pps Download paperwill finish at 2:50pm (ME seminar)
Thu Oct 22Invertibility of switched systemsDownload paper 
Tue Oct 27Gradient algorithms; introduction to hybrid controlgradient.ppsPaper 1, paper 2 
Thu Oct 29Hybrid control of nonholonomic systemsparking.ppsChapter 4 
Tue Nov 3Control with limited informationlimited-info.ppsSection 5.3  
Thu Nov 5Paper 1, paper 2  
Tue Nov 10Switching adaptive controlsupervisory.ppsChapter 6 
Thu Nov 12 
Tue Nov 17Final project presentations   
Thu Nov 19Final project presentations   
Tue Nov 24   no class: break
Thu Nov 26   no class: break
Tue Dec 1Final project presentations   
Thu Dec 3Final project presentations   
Tue Dec 8Final project presentations