Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen-Grossberg neural networks with uncertain external perturbations and mixed time delays

Abstract

This paper aims to investigate the synchronization control of a class of discontinuous fuzzy Cohen-Grossberg neural networks (DFCGNNs) with uncertain external perturbations and mixed time delays (discrete and distributed time-delays). By using functional differential inclusions theory, inequality technique and the non-smooth analysis of Lyapunov-Krasovskii functional, a simple switching adaptive control is designed and some new criteria are obtained to achieve the finite-time synchronization of the proposed drive-response systems. Besides, the upper bound of the settling time is estimated. Based on the finite-time synchronization, we further present a novel discontinuous state-feedback controller to the response neural system in order to derive the fixed-time synchronization criteria and estimate the settling time. Compared with the previous results which can only fixed-timely synchronize or finite-timely synchronize some simple delayed fuzzy neural network systems with continuous activation functions and without uncertain external perturbations, the DFCGNNs with uncertain external perturbations and mixed time delays addressed and the theoretical results of this paper are more generalized and inclusive. Finally, several simulation examples and remarks are provided to verify the correctness and advantages of the main results.