Exponential input-to-state stability for hybrid dynamical networks via impulsive interconnection

This paper investigates the problem of exponential input-to-state stability (e-ISS) for hybrid dynamical networks (HDN) via impulsive interconnection. New concepts of input-to-state exponent property (IS-E) and augmented time are proposed for dynamical systems and hybrid systems respectively. By using IS-E estimations of nodes in HDN and methods such as multiple Lyapunov functions and hybrid time, two types of e-ISS criteria for continuous-time/discrete-time HDN are established respectively. The requirements on ISS property of every subsystem and small-gain condition for interconnection in interconnected systems or networks in the literature is relaxed. The obtained e-ISS results are extended to the case of delayed impulsive interconnection. One representative example is given to illustrate the theoretical results.