Abstract

Hybrid dynamical systems combine continuous-time dynamics with discrete-time dynamics. They include physical systems that interact with discrete automata, mechanical systems that experience impacts, and various other types of systems with impulsive characteristics. Hybrid systems exhibit rich dynamical behavior, including some phenomena that do not appear in continuous-time or discrete-time systems acting alone. Nevertheless, many of the stability analysis tools that are available for classical dynamical systems, including Lyapunov theorems and the invariance principle, can be applied readily to hybrid dynamical systems. In this talk, we present a modeling framework for hybrid dynamical systems in which asymptotic stability enjoys some inherent robustness properties and is equivalent to the existence of a smooth Lyapunov function. We also describe additional stability analysis tools, including one based on an invariance principle for hybrid systems. Finally, we discuss some hybrid control algorithms that follow from the analysis tools described in the talk.