This paper investigates the problem of the finite-time synchronization of a class of coupled memristor-based recurrent neural networks (MRNNs) with time delays. Based on the drive-response concept and differential inclusions theory, several sufficient assumptions are given to ensure the finite-time synchronization of MRNNs. In order to realize the finite-time synchronization between the drive system and the response system, we design three classes of novel control rules such as static state controller, static output controller, dynamic state controller. Using the theory of differential inclusion, a generalized finite-time convergence theorem and Lyapunov method, the conditions herein are easy to be verified. Moreover, the upper bounds of the settling time of synchronization are estimated and the designed dynamic state controllers have good anti-interference capacity. Finally, two numerical examples are presented to illustrate the effectiveness and the validity of theoretical results.

中文翻译：

---

一类基于耦合忆阻器的递归神经网络的有限时间同步：静态控制和动态控制方法

本文研究了一类具有时间延迟的基于耦合忆阻器的递归神经网络 (MRNN) 的有限时间同步问题。基于驱动响应概念和微分包含理论，给出了几个充分的假设来确保 MRNN 的有限时间同步。为了实现驱动系统和响应系统的有限时间同步，我们设计了静态控制器、静态输出控制器、动态控制器三类新颖的控制规则。利用微分包含理论、广义有限时间收敛定理和李雅普诺夫方法，这里的条件很容易得到验证。而且，估计了同步建立时间的上限，设计的动态控制器具有良好的抗干扰能力。最后，给出了两个数值例子来说明理论结果的有效性和有效性。