Network packet

Fuzzy control system

Control (management)

Biology

Statistics

Encryption

Probabilistic logic

Transmission delay

Computer science

Controller (irrigation)

Secure communication

Computer network

Kernel (algebra)

Mathematics

Fuzzy logic

Agronomy

Synchronization (alternating current)

Artificial intelligence

Combinatorics

Probability density function

Channel (broadcasting)

Control theory (sociology)

Artificial neural network

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