This research investigates the stability of discrete-time neural networks (DNNs) with a time-varying delay by using the Lyapunov-Krasovskii functional (LKF) method. Recent researches acquired some less conservatism stability criteria for time-varying delayed systems via some augmented LKFs. However, the forward difference of such LKFs resulted in high-degree time-varying delay-dependent polynomials. This research aims to develop some augmented state-related vectors and the corresponding extended free-weighting matrices zero equations to avoid the appearance of such high-degree polynomials and help to provide more freedom for the estimation results. Besides, an augmented delay-product-type LKF is also established for ameliorating the stability conditions of the time-varying delayed DNNs. Then, based on the above methods and Jensen's summation inequality, the auxiliary-function-based summation inequality, and the reciprocally convex matrix inequality, some less conservatism stability criteria for time-varying delayed DNNs are formulated. The validity of the proposed time-varying delay-dependent stability criteria is illustrated by two numerical examples.

中文翻译：

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具有时变延迟的离散时间神经网络的稳定性分析：扩展的自由加权矩阵零方程方法。

本研究使用 Lyapunov-Krasovskii 泛函 (LKF) 方法研究具有时变延迟的离散时间神经网络 (DNN) 的稳定性。最近的研究通过一些增强的 LKF 获得了时变延迟系统的一些不太保守的稳定性标准。然而，这种 LKF 的前向差异导致了高度时变延迟相关多项式。本研究旨在开发一些增强的状态相关向量和相应的扩展自由加权矩阵零方程，以避免此类高次多项式的出现，并有助于为估计结果提供更大的自由度。此外，还建立了一种增强的延迟积型 LKF，用于改善时变延迟 DNN 的稳定性条件。然后，基于上述方法和 Jensen' s 求和不等式、基于辅助函数的求和不等式和倒数凸矩阵不等式，制定了一些用于时变延迟 DNN 的不太保守的稳定性标准。所提出的时变延迟相关稳定性准则的有效性通过两个数值示例来说明。