In this paper, a class of Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with time-varying delays are considered. Initially, the sufficient conditions are proposed to ascertain the existence and uniqueness of the solutions for the considered dynamical system via homeomorphism mapping principle. Then synchronization of the considered delayed neural networks is analyzed by utilizing the drive-response (master-slave) concept, in terms of a linear matrix inequality (LMI), the Lyapunov-Krasovskii (LK) functional, and also using some free weighting matrices. Next, this result is extended so as to establish the robust synchronization of a class of delayed CGFCNNs with polytopic uncertainty. Sufficient conditions are proposed to ascertain that the considered delayed networks are robustly synchronized by using a parameter-dependent LK functional and LMI technique. The restriction on the bounds of derivative of the time delays to be less than one is relaxed. In particular, the concept of fuzzy theory is greatly extended to study the synchronization with polytopic uncertainty which differs from previous efforts in the literature. Finally, numerical examples and simulations are provided to illustrate the effectiveness of the obtained theoretical results.

中文翻译：

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具有时变时滞的Cohen-Grossberg模糊细胞神经网络的同步

本文考虑一类具有时变时滞的Cohen-Grossberg模糊细胞神经网络（CGFCNN）。最初，提出了充分的条件，以通过同胚映射原理确定所考虑动力系统解的存在性和唯一性。然后根据线性矩阵不等式（LMI），Lyapunov-Krasovskii（LK）泛函，利用驱动响应（主从）概念，分析所考虑的延迟神经网络的同步，并使用一些自由加权矩阵。接下来，扩展该结果，以建立具有多主题不确定性的一类延迟CGFCNN的鲁棒同步。提出了充分的条件来确定所考虑的延迟网络通过使用依赖于参数的LK功能和LMI技术进行鲁棒同步。放宽对时间延迟的导数范围的限制，使其小于1。尤其是，模糊理论的概念已得到很大扩展，以研究多面体不确定性的同步性，这与文献中先前所做的努力不同。最后，通过数值算例和仿真来说明所获得理论结果的有效性。