Hybrid stability analysis via extended small-gain theorem for networked cyber-physical systems with transmission delay

Abstract

This paper deals with hybrid stability analysis for networked cyber-physical systems with time delays and impulsive control. We use a thermodynamic framework to model the networked cyber-physical system (CPS) with a time delay and propose a hybrid controller to stabilize such a time-delay CPS. We consider the case where the time delay happened in the transmission process, thus the CPS has a nonlinear delayed part. Each subsystem in the networked CPS is assumed to evolve according to its controller and exchange delayed state information with its neighboring subsystems. Next, we extend the nonlinear input-to-state stability (ISS) small-gain theorem to networked CPS systems. Specifically, we render each subsystem in the networked CPS to have an interconnected ISS property first; and the input for the subsystem is the delayed information from its neighbors. Then hybrid stability of the whole networked CPS can be guaranteed based on this extended small-gain theorem.