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.

中文翻译：

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具有不确定外部扰动和混合时滞的不连续模糊 Cohen-Grossberg 神经网络的有限时间和固定时间同步控制

摘要 本文旨在研究一类具有不确定外部扰动和混合时延（离散和分布式时延）的不连续模糊 Cohen-Grossberg 神经网络（DFCGNNs）的同步控制。通过使用泛函微分包含理论、不等式技术和Lyapunov-Krasovskii泛函的非光滑分析，设计了一种简单的切换自适应控制，并获得了一些新的准则来实现所提出的驱动响应系统的有限时间同步。此外，估计稳定时间的上限。基于有限时间同步，我们进一步向响应神经系统提出了一种新颖的不连续状态反馈控制器，以推导出固定时间同步标准并估计稳定时间。与以往只能固定时间同步或有限时间同步一些具有连续激活函数且没有不确定外部扰动的简单延迟模糊神经网络系统的结果相比，解决了具有不确定外部扰动和混合时间延迟的 DFCGNNs 的理论结果这篇论文更具概括性和包容性。最后，给出了几个仿真实例和备注，以验证主要结果的正确性和优势。解决了具有不确定外部扰动和混合时间延迟的 DFCGNNs，本文的理论结果更具概括性和包容性。最后，给出了几个仿真实例和备注，以验证主要结果的正确性和优势。解决了具有不确定外部扰动和混合时间延迟的 DFCGNNs，本文的理论结果更具概括性和包容性。最后，给出了几个仿真实例和备注，以验证主要结果的正确性和优势。