W.P.M.H. Heemels, B. De Schutter, J. Lunze, and M. Lazar, "Stability analysis and controller synthesis for hybrid dynamical systems," Philosophical Transactions of the Royal Society A, vol. 368, no. 1930, p. 4937-4960, Nov. 2010.
Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially profound in many technological systems in which logic decision making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical, and economical systems the usage of hybrid models is indispensable to adequately describe their behavior. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modeling, analysis, and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.