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This paper aims to study the impact of discontinuous activations, neutral-type operators, and mixed time delays on the finite-time and fixed-time robust synchronization of fuzzy neural networks. By using functional differential inclusions theory, inequality technique, and the non-smooth analysis of the Lyapunov-Krasovskii functional, a simple switching adaptive controller and a switching state-feedback controller are designed, some new criteria are obtained to achieve the finite-time and fixed-time synchronization of the proposed drive-response systems. Besides, the upper bound of the settling time of finite-time synchronization is estimated, and the settling time of fixed-time synchronization can be given in advance. In spite of many previous results on the synchronization of fuzzy neutral-type neural network and stability analysis of neural networks of neutral-type in Hale’s form with continuous activation functions, few references on the stability and synchronization control analysis of the neural network like the form of the neural network model addressed in this paper can be cited. From this point of view, the neural network model considered and the theoretical results of this paper are more generalized and inclusive. Finally, the simulation examples and remarks have been shown to verify the correctness and advantages of our main results.

Finite-Time and Fixed-Time Synchronization Criteria for Discontinuous Fuzzy Neural Networks of Neutral-Type in Hale’s Form