New conditions on synchronization of memristor-based neural networks via differential inclusions

•We analyze the exponential synchronization of the memristor-based networks.•We present the Filippov-framework and some new analytic techniques.•We provide an estimation of the exponential synchronization rate.

In this paper, a general framework named Filippov-framework and some new analytic techniques are presented for dealing with the exponential synchronization of memristor-based neural network system with time-varying delay. Several new sufficient conditions are established to guarantee two different types of exponential synchronization of the coupled networks based on master–slave (drive-response) concept and discontinuous state-feedback controller. In addition, we also provide an estimation of the exponential synchronization rate which depends on the time delay and system parameters. These conditions are good improvement and extension of the existing works on synchronization control of memristive or switching networks. Finally, the validity of our method and theoretical results is demonstrated by concrete examples with numerical simulations.