Exponential Synchronization for Discrete-Time Delayed Neural Networks via Memory-Based Saturated Controller

This paper investigates the local exponential synchronization for discrete-time neural networks containing the time-varying delay via the memory-based saturated controller. Using the modified sector condition, the augmented Lyapunov-Krasovskii functional and two recent inequalities, a synchronization criterion is first obtained by means of linear matrix inequalities such that the closed-loop error dynamics is locally exponentially stable. For the constant delay case, a simplified criterion is also proposed. Then, the optimization problems concerning the admissible initial condition set are specifically formulated. Finally, simulation results are presented to demonstrate the validity and reduced conservatism of the obtained results.