New results on exponential synchronization of memristor-based neural networks with discontinuous neuron activations

This paper investigates the exponential synchronization of delayed memristor-based neural networks (MNNs) with discontinuous activation functions. Based on the framework of Filippov solution and differential inclusion theory, using new analytical techniques and introducing suitable Lyapunov functionals, some novel sufficient conditions ensuring the exponential synchronization of considered networks are established via two types of discontinuous controls: linear feedback control and adaptive control. In particular, we extend the discontinuous control strategies for neural networks with continuous dynamics to MNNs with discontinuous activations. Numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized MNN circuits involving discontinuous activations and time-varying delays.