Event-Triggered Finite-Time Stabilization of Fuzzy Neural Networks With Infinite Time Delays and Discontinuous Activations

This article unifies the stability criteria of asymptotic, exponential, and finite-time control within a single framework for fuzzy neural networks (FNNs) with infinite time delays. First, the boundedness and differentiability for time delays are removed. Then, Lipschitz condition for activation function is relaxed, which is allowed to have jumping discontinuous points. To stabilize FNNs, the analytical method is established by comparison principle, contradiction method and inequality techniques. Moreover, different from the traditional Lyapunov method and finite-time stability theorem, several sufficient conditions are deduced and the suppression functions are designed to guarantee asymptotic, exponential, and finite-time stabilization for FNNs by adjusting the parameters of the same controller. There is not necessary to construct the complex integral-type Lyapunov functional to deal with infinite time delays and to design power function in controller for finite-time stabilization. In addition, the designed event-triggered mechanism has the inherent advantages of saving communication resources and indirectly eliminates the chattering caused by signum function. Finally, simulations are presented to illustrate the feasibility and effectiveness of the theoretical results.