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ECE 586 DL: Hybrid Systems and Control (Fall 2018)

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 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, room 4070, ECE Building.

Instructor: Daniel Liberzon.
Office: 144 CSL.
Email: liberzon at
Office hours: see me after class

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. 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 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 Aug 28Introduction to switched and hybrid systemsintro.ppsxSection 1.1
Thu Aug 30Solutions of switched and hybrid systemsnone Section 1.2
Tue Sep 4Stability: definitions and background resultsnone Appendix A
Thu Sep 6Stability under arbitrary switching and
common Lyapunov functions
GUAS.ppsxSections 2.1.1-2.1.3
Tue Sep 11noneSections 2.1.4, 2.1.5
Thu Sep 13Commutation relations and
stability of switched systems
LA.ppsxSection 2.2, Appendix B
Tue Sep 18Paper 1, paper 2, paper 3
Thu Sep 20Systems with special structurestructure.ppsxSection 2.3
Tue Sep 25Common weak Lyapunov functions; observabilityobservability.ppsxDownload paper
Thu Sep 27Multiple Lyapunov functions and dwell-time switchingconstrained.ppsxSections 3.1, 3.2
Tue Oct 2No class: Allerton conference (tutorial sessions)
Thu Oct 4 No class: Allerton conference
Tue Oct 9Average dwell time; multiple weak Lyapunov functions;
state-dependent switching
constrained.ppsxSections 3.2-3.4, paper
Thu Oct 11Input-to-state stability of switched systemsISS-invertibility.ppsx Paper 1, paper 2
Tue Oct 16Invertibility of switched systemsDownload paper
Thu Oct 18Gradient algorithmsgradient.ppsxPaper 1, paper 2
Tue Oct 23Introduction to hybrid control;
hybrid control of nonholonomic systems
parking.ppsxChapter 4
Thu Oct 25
Tue Oct 30Control with limited informationlimited-info.ppsxSection 5.3
Thu Nov 1Paper 1, paper 2, paper 3
Tue Nov 6Limited data-rate control of switched systemsswitched-quantized.ppsxDownload paper
Thu Nov 8Switching adaptive controlsupervisory.ppsxChapter 6
Tue Nov 13
Thu Nov 15
Tue Nov 20No class: Thanksgiving break
Thu Nov 22No class: Thanksgiving break
Tue Nov 27Final project presentations
Thu Nov 29Final project presentations
Tue Dec 4Final project presentations
Thu Dec 6Final project presentations
Tue Dec 11Final project presentations