IEEE Trans Neural Netw Learn Syst. 2021 Aug;32(8):3690-3699. doi: 10.1109/TNNLS.2020.3015944. Epub 2021 Aug 3.
This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays (DMNNs). By means of inequality techniques, theories of the M-matrix, and the comparison strategy, the Lagrange exponential stability of the underlying DMNNs is considered in the sense of Filippov, and the globally exponentially attractive set is estimated through employing the M-matrix and external input. Especially, when the external input is not concerned, the Lyapunov exponential stability of the corresponding DMNNs is developed immediately in the form of an M-matrix, which contains some published outcomes as special cases. Furthermore, by constructing an M-matrix-based differential system, the Lyapunov exponential stability of the DMNNs is studied, which is less conservative than some existing ones. Finally, three simulation examples are carried out to examine the validness of the theories.
本文研究了具有离散和分布时变时滞的忆阻神经网络（DMNNs）的拉格朗日指数稳定性和李雅普诺夫指数稳定性。通过不等式技术、M-矩阵理论和比较策略，从 Filippov 的意义上考虑了基础 DMNNs 的拉格朗日指数稳定性，并通过使用 M-矩阵和外部输入来估计全局指数吸引集。特别是，当不考虑外部输入时，以 M-矩阵的形式直接得到相应 DMNNs 的李雅普诺夫指数稳定性，其中包含了一些已发表的结果作为特例。此外，通过构建基于 M-矩阵的微分系统，研究了 DMNNs 的李雅普诺夫指数稳定性，该方法比一些现有方法更为保守。最后，通过三个仿真示例验证了理论的有效性。
