UE Discrete event systems

Degrees incorporating this pedagocial element :


This course is an introduction to hybrid systems, i.e. dynamic systems that exhibits both continuous and discrete dynamic behavior. The first part of the course introduces several paradigms for modelling hybrid systems: switched systems, piecewise smooth systems, hybrid automata. These notions are illustrated by examples. The second part of the course deals with Lyapunov techniques for stability analysis and stabilization of hybrid systems and the related numerical techniques such as LMI formulations. The third part of the course deals with abstraction techniques for the symbolic analysis and control of hybrid systems.

 Switched systems, piecewise smooth systems, sliding mode, hybrid automata, blocking and deterministic systems, Zeno behaviors. 
Stability and stabilization 
 Common and multiple Lyapunov functions, dwell time, LMI formulation and S-procedure, stabilization by switching. 
Abstraction based control 
 Transition systems, simulation relation, reachability analysis, safety controller synthesis. 
Lab 1 LMI techniques for stability analysis and stabilization 
Lab 2 Abstraction based control


  • J. Lunze and F. Lamnabhi-Lagarrigue (Eds), Handbook of hybrid systems control: theory, tools, applications, Cambridge University Press, 2009.
  • D. Liberzon, Switching in systems and control, Birkhäuser Basel, 2003.
  • P. Tabuada, Verification and control of hybrid systems: a symbolic approach, Springer, 2009