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A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.amc.2020.125401
Zeyu Dong , Xin Wang , Xian Zhang

Abstract This paper focuses on the problem of global exponential stability analysis for high-order delayed discrete-time Cohen–Grossberg neural networks. Multiple time-varying delays are considered. First, a technique lemma is obtained based on the properties of nonsingular M-matrices. Second, the delay-dependent and -independent criteria under which the zero equilibrium is globally exponentially stable are derived, respectively. Last, the validity of these criteria are illustrated by a pair of numerical examples. Compared with the previous results, the merits of the proposed method are: (i) no Lyapunov–Krasovskii functional or auxiliary function is required; (ii) less computational complexity is verified; and (iii) the obtained stability criteria can easily be realized, since they are to test whether a matrix is nonsingular M-matrix.

中文翻译:

高阶延迟离散时间 Cohen-Grossberg 神经网络的基于非奇异 M 矩阵的全局指数稳定性分析

摘要 本文重点研究高阶延迟离散时间 Cohen-Grossberg 神经网络的全局指数稳定性分析问题。考虑了多个时变延迟。首先,基于非奇异M矩阵的性质获得技术引理。其次,分别推导出零平衡全局指数稳定的延迟相关和独立的标准。最后,通过一对数值例子说明了这些标准的有效性。与之前的结果相比,该方法的优点是:(i)不需要Lyapunov-Krasovskii泛函或辅助函数;(ii) 验证较少的计算复杂度;(iii) 获得的稳定性标准很容易实现,因为它们是为了测试矩阵是否是非奇异的 M 矩阵。
更新日期:2020-11-01
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