Exponential ${\rm H}_{\infty}$ Synchronization of General Discrete-Time Chaotic Neural Networks With or Without Time Delays

This brief studies exponential H∞ synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H∞ control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H∞ norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H∞ synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.