1. INTRODUCTION to SWITCHED and HYBRID SYSTEMS Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign

2. electric circuit SWITCHED and HYBRID SYSTEMS Hybrid systems combine continuous and discrete dynamics Which practical systems are hybrid? Which practical systems are not hybrid? More tractable models of continuous phenomena thermostat stick shift walking cell division

3. MODELS of HYBRID SYSTEMS … [ Van der Schaft–Schumacher ’00 ] [ Proceedings of HSCC ] continuous discrete [ Nešić–L ‘05 ]

4. SWITCHED vs. HYBRID SYSTEMS Switched system: is a family of systems is a switching signal Switching can be: State-dependent or time-dependent Autonomous or controlled Details of discrete behavior are “abstracted away” : stability and beyondProperties of the continuous state Discrete dynamics classes of switching signals