This paper investigates finite-time synchronization for fuzzy Cohen–Grossberg neural networks (FCGNNs) with mixed delays and discontinuous activations via state-feedback control. The features of FCGNNs, discrete time delays, distributed delays and discontinuous activations are taken into account which makes our networks more general and practical in comparison with the most existing Cohen–Grossberg neural networks. Two switching state-feedback controllers designed for the implement of finite-time synchronization can be used to effectively overcome the limitations of the traditional continuous linear feedback controllers. Different from previous work, graph theory and Lyapunov method are used to study finite-time synchronization of FCGNNs for the first time in this paper, then some sufficient criteria are obtained to guarantee the finite-time synchronization of FCGNNs. In particular, it is worth noting that the settling time for finite-time synchronization is closely related to the topological structure of FCNNs. Finally, two numerical examples are given to verify the feasibility and effectiveness of the theoretical results.

中文翻译：

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具有混合延迟和不连续激活的模糊Cohen-Grossberg神经网络有限时间同步的图论方法

本文研究了带有状态延迟控制的混合时滞和不连续激活的模糊Cohen-Grossberg神经网络（FCGNN）的有限时间同步。考虑到FCGNN的功能，离散时间延迟，分布式延迟和不连续激活，这使我们的网络与大多数现有的Cohen-Grossberg神经网络相比更加通用和实用。为实现有限时间同步而设计的两个开关状态反馈控制器可用于有效克服传统连续线性反馈控制器的局限性。与以前的工作不同，本文首次使用图论和Lyapunov方法研究FCGNN的有限时间同步，然后获得了足够的标准来保证FCGNN的有限时间同步。特别要注意的是，有限时间同步的建立时间与FCNN的拓扑结构密切相关。最后，通过两个数值例子验证了理论结果的可行性和有效性。