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ECE 586 DL: Hybrid Systems and Control (Spring 2023)

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 they have attracted considerable attention in the control literature. This advanced graduate-level course will introduce the students to analysis and design of switched and hybrid systems. The selection of specific topics is heavily influenced by the research of the instructor and his collaborators, drawn from his 2003 research monograph and more recent research articles.



Schedule: Tue Thu 12:30-1:50pm, room 3081, ECE Building.

Instructor: Daniel Liberzon.
Office: 144 CSL.
Email: liberzon at
Office hours: TBD

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, on, and through SpringerLink here (university login required). The textbook material will be supplemented by recent research articles.

Final project: This course will involve a final project presentation towards the end of the semester. Details will be explained in class. There will be no required homework or 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 Reading
Tue Jan 17Introduction to switched and hybrid systemsintro.ppsxSection 1.1
Thu Jan 19Solutions of switched and hybrid systemsnone Section 1.2
Tue Jan 24Stability: definitions and background resultsnone Appendix A
Thu Jan 26Uniform stability and common Lyapunov functionsGUAS.ppsxSections 2.1.1-2.1.3
Tue Jan 31Uniform stability of switched linear systemsnoneSections 2.1.4, 2.1.5
Thu Feb 2Commutation relations and
stability of switched systems
LA.ppsxSection 2.2, Appendix B
Tue Feb 7Paper 1, paper 2, paper 3
Thu Feb 9Systems with special structurestructure.ppsxSection 2.3
Tue Feb 14Common weak Lyapunov functions; observabilityobservability.ppsxDownload paper
Thu Feb 16Multiple Lyapunov functions and dwell-time switchingconstrained.ppsxSections 3.1, 3.2
Tue Feb 21Guest lecture by Prof. Rafal Goebel, Loyola University Chicago
Thu Feb 23Average dwell time; multiple weak Lyapunov functions; state-dependent switchingconstrained.ppsxSections 3.2-3.4, paper
Tue Feb 28Input-to-state stability of switched systemsISS-invertibility.ppsx Paper 1, paper 2
Thu Mar 2Invertibility of switched systemsDownload paper
Tue Mar 7Introduction to hybrid control;
hybrid control of nonholonomic systems
parking.ppsxChapter 4
Thu Mar 9
Tue Mar 14No class: Spring break
Thu Mar 16No class: Spring break
Tue Mar 21Control with limited informationlimited-info.ppsxSection 5.3
Thu Mar 23 (Zoom)Paper 1, paper 2, paper 3
Tue Mar 28No class: DL out of town
Thu Mar 30No class: DL out of town
Thu Apr 4Switching adaptive controlsupervisory.ppsxChapter 6
Tue Apr 6
Tue Apr 11Gradient algorithmsgradient.ppsxPaper 1, paper 2
Thu Apr 13Final project presentations
Tue Apr 18Final project presentations
Thu Apr 20Limited data-rate control of switched systemsswitched-quantized.ppsxDownload paper
Tue Apr 25Final project presentations
Thu Apr 27Final project presentations
Tue May 2Final project presentations