ECE 586 Home Page

ECE 586 DL: Hybrid Systems and Control (Fall 2013)

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.



Schedule: Tue Thu 2-3:20pm, 1103 Siebel Center for Computer Science.

Instructor: Daniel Liberzon.
Office: 144 CSL.
Email: liberzon at
Office hours: Thursdays 3:30-4:30pm.

Prerequisites: 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 Also available as PDF download from SpringerLink (subscription access from UIUC). 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 and/or written presentation towards the end of the semester. There will be no exams.


This course syllabus will be populated and updated as the semester progresses. (Click here for a complete syllabus from the previous offering of this course.) All section and page numbers in the "reading" column refer to the textbook unless otherwise noted.

Date TopicSlides ReadingNotes
Tue Aug 27Introduction to switched and hybrid systemsintro.ppsxSection 1.1
Thu Aug 29   no class (DL out of town)
Tue Sep 3 no class (DL out of town)
Thu Sep 5 no class (DL out of town)
Tue Sep 10Solutions of switched and hybrid systems noneSection 1.2  
Thu Sep 12Stability: definitions and background results noneAppendix A
Tue Sep 17Stability under arbitrary switching and
common Lyapunov functions
GUAS.ppsxSections 2.1.1-2.1.3 
Thu Sep 19noneSections 2.1.4, 2.1.5
Tue Sep 24Commutation relations and
stability of switched systems
LA.ppsxSection 2.2, Appendix B 
Thu Sep 26Paper 1, paper 2 
Tue Oct 1Systems with special structurestructure.ppsxSection 2.3 
Thu Oct 3   no class: Allerton conference
Tue Oct 8Common weak Lyapunov functions; observabilityobservability.ppsxDownload paper 
Thu Oct 10Multiple Lyapunov functions and dwell-time switchingconstrained.ppsxSections 3.1, 3.2, paper  
Tue Oct 15Average dwell time; multiple weak Lyapunov functions
Thu Oct 17State-dependent switchingSections 3.3, 3.4 
Tue Oct 22Input-to-state stability of switched systemsISS-invertibility.ppsx Paper 1, paper 2
Thu Oct 24Invertibility of switched systemsDownload paper 
Tue Oct 29Gradient algorithms; introduction to hybrid controlgradient.ppsxPaper 1, paper 2 
Thu Oct 31Hybrid control of nonholonomic systemsparking.ppsxChapter 4 
Tue Nov 5Control with limited informationlimited-info.ppsxSection 5.3  
Thu Nov 7Paper 1, paper 2 will finish at 3:00pm 
Tue Nov 12Switching adaptive controlsupervisory.ppsxChapter 6 
Thu Nov 14 
Tue Nov 19Final project presentations   
Thu Nov 21Final project presentations   
Tue Nov 26   no class: break
Thu Nov 28   no class: break
Tue Dec 3Final project presentations   
Thu Dec 5Final project presentations   
Tue Dec 10Final project presentations