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.

中文翻译：

---

具有混合时变延迟的忆阻神经网络的全局指数稳定性

本文研究了具有离散和分布式时变延迟的忆阻神经网络 (DMNN) 的拉格朗日指数稳定性和 Lyapunov 指数稳定性。通过不等式技术、M矩阵理论和比较策略，在Filippov的意义上考虑了底层DMNNs的拉格朗日指数稳定性，并通过使用M矩阵和外部估计全局指数吸引集输入。特别是，当不考虑外部输入时，相应 DMNN 的 Lyapunov 指数稳定性立即以 M 矩阵的形式发展，其中包含一些已发表的结果作为特殊情况。此外，通过构建基于 M 矩阵的微分系统，研究了 DMNN 的 Lyapunov 指数稳定性，这比一些现有的更不保守。最后，通过三个仿真实例来检验理论的有效性。