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ECE 586 DL: Hybrid Systems and Control (Fall 2015)

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 3081, ECE Building.

Instructor: Daniel Liberzon.
Office: 144 CSL.
Email: liberzon at
Office hours: Thursdays immediately after clas.

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 25Introduction to switched and hybrid systemsintro.ppsxSection 1.1
Thu Aug 27Solutions of switched and hybrid systems noneSection 1.2
Tue Sep 1Stability: definitions and background results noneAppendix A
Thu Sep 3Stability under arbitrary switching and
common Lyapunov functions
GUAS.ppsxSections 2.1.1-2.1.3
Tue Sep 8noneSections 2.1.4, 2.1.5
Thu Sep 10Commutation relations and
stability of switched systems
LA.ppsxSection 2.2, Appendix B
Tue Sep 15Paper 1, paper 2
Thu Sep 17Systems with special structurestructure.ppsxSection 2.3
Tue Sep 22Common weak Lyapunov functions; observabilityobservability.ppsxDownload paper
Thu Sep 24Multiple Lyapunov functions and dwell-time switchingconstrained.ppsxSections 3.1, 3.2, paper
Tue Sep 29Average dwell time; multiple weak Lyapunov functions
Thu Oct 1 No class: Allerton conference
Tue Oct 6State-dependent switchingconstrained.ppsxSections 3.3, 3.4
Thu Oct 8Input-to-state stability of switched systemsISS-invertibility.ppsx Paper 1, paper 2
Tue Oct 13Invertibility of switched systemsDownload paper
Thu Oct 15Gradient algorithmsgradient.ppsxPaper 1, paper 2
Tue Oct 20Introduction to hybrid control;
hybrid control of nonholonomic systems
parking.ppsxChapter 4
Thu Oct 22
Tue Oct 27Control with limited informationlimited-info.ppsxSection 5.3
Thu Oct 29Paper 1, paper 2
Tue Nov 3Limited data-rate control of switched systems;
multi-agent coordination with quantized sensing
switched-quantized.ppsxDownload paper
Thu Nov 5polygons.pdfPaper 1, paper 2
Tue Nov 10Switching adaptive controlsupervisory.ppsxChapter 6
Thu Nov 12
Tue Nov 17Final project presentations
Thu Nov 19Final project presentations
Tue Nov 24No class: Thanksgiving break
Thu Nov 26No class: Thanksgiving break
Tue Dec 1Final project presentations
Thu Dec 3Final project presentations
Tue Dec 8Final project presentations