Interconnected jumping time-delay systems: Mode-dependent decentralized stability and stabilization

Abstract

In this paper, we deal with the problems of mode-dependent decentralized stability and stabilization with H ∞ performance for a class of continuous-time interconnected jumping time-delay systems. The jumping parameters are governed by a finite state Markov process and the delays are unknown time-varying and mode-dependent within interval. The interactions among subsystems satisfy quadratic bounding constraints. To characterize mode-dependent local stability behavior, we employ an improved Lyapunov-Krasovskii functional at the subsystem level and express the stability conditions in terms of linear matrix inequalities (LMIs). A class of local decentralized state-feedback controllers is developed to render the closed-loop interconnected jumping system stochastically stable. Then, we extend the feedback strategy to dynamic observer-based control and establish the stochastic stabilization via LMIs. It has been established that the developed results encompass several existing results as special cases which are illustrated by simulation of examples. © 2011 John Wiley & Sons, Ltd.