Finite-time Synchronization of a Class of Coupled Memristor-based Recurrent Neural Networks: Static State Control and Dynamic Control Approach

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.