This paper first puts forward the concept of global polynomial stabilization (GPS) of coupled neural networks (CNNs) with multi‐proportional delays. First, the existence and uniqueness of the equilibrium point of the proposed CNNs are proved by using homeomorphic mapping theorem. Second, by taking discrete controller, based on Lyapunov functionals and linear matrix inequality (LMI) skills, we gain several delay‐dependent GPS and global asymptotic stabilization (GAS) criteria for the proposed system, and these criteria can be validated by Matlab. The relationship among GPS, global exponential stabilization (GES), and GAS is also revealed. In the end, our results are confirmed by examples.

中文翻译：

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具有多比例延迟的耦合神经网络的全局多项式镇定和全局渐近镇定

本文首先提出了具有多比例延迟的耦合神经网络（CNN）的全局多项式稳定（GPS）的概念。首先，利用同胚映射定理证明了所提出的CNN平衡点的存在性和唯一性。其次，通过采用离散控制器，基于Lyapunov函数和线性矩阵不等式（LMI）技能，我们为拟议系统获得了一些依赖于延迟的GPS和全局渐近稳定（GAS）标准，并且这些标准可以通过Matlab进行验证。还揭示了GPS，全局指数稳定（GES）和GAS之间的关系。最后，通过实例证实了我们的结果。