On asymptotic synchronization of interconnected hybrid systems with applications

In this paper, we consider the synchronization of the states of a multiagent network system, where each agent exhibits hybrid behavior. Specifically, the state of each agent may evolve continuously according to a differential inclusion, and, at times, jump discretely according to a difference inclusion. We develop a notion of asymptotic synchronization for part of the state of the system. Our definition of asymptotic synchronization imposes both Lyapunov stability and attractivity on the difference between the agents' states. We recast synchronization as a set stabilization problem, for which tools for the study of asymptotic stability of sets for hybrid systems are suitable. As applications, we introduce two synchronization problems for hybrid systems: the interconnection of continuous-time systems connected over an intermittent communication network and the synchronization of interconnected impulse-coupled oscillators.