Combinatorics

Channel (broadcasting)

Probability density function

Computer network

Mathematics

Agronomy

Kernel (algebra)

Biology

Statistics

Transmission delay

Network packet

Encryption

Artificial intelligence

Fuzzy control system

Controller (irrigation)

Control (management)

Synchronization (alternating current)

Computer science

Probabilistic logic

Secure communication

Control theory (sociology)

Artificial neural network

Fuzzy logic

IEEE Transactions on Fuzzy Systems

In this article, we study 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 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.

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