Synchronization of Delayed Fuzzy Neural Networks with Probabilistic Communication Delay and Its Application to Image Encryption

Abstract

This article studies the design of fuzzy synchronization controller of Takagi—Sugeno (T-S) fuzzy neural networks with distributed time-varying delay and probabilistic network communication delay. Compared with the existing model of neural networks with distributed time-varying delay without kernel, a more general model containing a distributed delay kernel is considered. By utilizing the probability distribution of random communication delays, a distributed but deterministic delay model is established. In this model, the delay probability density function is treated as the distributed delay kernel. By developing a new Lyapunov-Krasovskii functional (LKF) related to the distributed delay kernels and using an integral inequality, new sufficient conditions for the existence of a synchronization controller are presented. Finally, a numerical simulation and an application of encrypting the image are carried out to illustrate the effectiveness of the developed strategy.