This article tackles the global exponential stability for a class of delayed complex-valued inertial neural networks in a discrete-time form. It is assumed that the activation function can be separated explicitly into the real part and imaginary part. Two methods are employed to deal with the stability issue. One is based on the reduced-order method. Two exponential stability criteria are obtained for the equivalent reduced-order network with the generalized matrix-measure concept. The other is directly based on the original second-order system. The main theoretical results complement each other. Some comparisons with the existing works show that the results in this article are less conservative. Two numerical examples are given to illustrate the validity of the main results.

中文翻译：

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关于延迟离散时间复值惯性神经网络的指数稳定性

本文以离散时间形式解决了一类延迟复值惯性神经网络的全局指数稳定性。假设激活函数可以明确地分为实部和虚部。采用两种方法来处理稳定性问题。一种是基于降阶方法。对于具有广义矩阵测度概念的等效降阶网络，获得了两个指数稳定性标准。另一种是直接基于原有的二阶系统。主要理论结果相辅相成。与现有作品的一些比较表明，本文的结果不太保守。给出了两个数值例子来说明主要结果的有效性。