Control of Hybrid Systems: An Overview of Recent Advances

This chapter presents a unified overview of recent results on controlling hybrid dynamical systems. The first section of the chapter introduces basic notation and definitions, as well as the modeling framework. The second section pertains to stabilization of sets for hybrid systems, stabilizability and control Lyapunov functions. The third section presents conditions guaranteeing the existence of continuous static state feedback controllers. The fourth section introduces the notion of passivity, links it to asymptotic stability and presents sufficient conditions useful in the design of passivity-based controllers. The final section states a tracking control problem for hybrid systems and presents design conditions for tracking controllers. © 2013 by John Wiley & Sons, Inc