H∞ synchronization for a class of discrete-time nonlinear systems with interval time-varying delays

This paper investigates the H_∞ synchronization problem for two discrete time-varying-delayed nonlinear systems such as Hopfield neural networks, complex systems, recurrent multilayer perceptrons (RMLPs), Chua´s circuits etc., which can be transformed into the unified model consisting of a linear dynamic system and a static nonlinear operator. Throughout the paper, first a response system is established according to the drive-response concept. Second, the H_∞ performance for the synchronization error dynamical system between the drive model and the response model is analyzed based on the Lyapunov stability theory and linear matrix inequality (LMI) technique. Then, based on the analysis, a state feedback controller is designed to guarantee the H_∞ performance for the synchronization error dynamical system. During the design procedure, novel Lyapunov functions are established to increase the upper bounds of the time-varying delays with their lower bounds fixed such that the conservatism of conditions for the feedback controller synthesis is reduced. Finally an illustrative example is provided to verify the effectiveness of the proposed control laws.