Study of finite-time synchronization between memristive neural networks with leakage and mixed delays

This article investigates the finite-time synchronization (FTS) of memristive neural networks (MNNs) with leakage and mixed delays by using state feedback and adaptive control techniques. The solution of all the systems has been obtained in the Filippov sense using theories of differential inclusion and set-valued maps. To assure the synchronization of memristive neural networks, a few sufficient conditions based on the Filippov solution and Lyapunov functional technique rather than the finite-time stability theorem have been obtained. In order to achieve synchronization within finite time, a discontinuous state feedback controller has been constructed, and settling time has been determined explicitly. A novel adaptive controller has been constructed to minimize the control gain. The numerical examples authenticate the efficacy of the theoretic outcomes.