Sliding mode exponential H∞ synchronization of Markovian jumping master-slave systems with time-delays and nonlinear uncertainties

This paper investigates the problem of exponential H_∞ synchronization for a class of master-slave systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law which include the master-slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H_∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H_∞ synchronization of the two coupled master and slave systems regardless of their initial states. A numerical example is given to show the effectiveness of the method.