Finite-time synchronization of fractional-order memristive recurrent neural networks with discontinuous activation functions

This paper is concerned with the finite-time synchronization for a class of drive-response fractional-order memristive recurrent neural networks with discontinuous activation functions. By using the theories of fractional-order differential inclusions and set-valued map, the finite-time synchronization problem for a class of drive-response fractional-order memristive recurrent neural networks with discontinuous activation functions is formulated under the framework of Filippov solution. Then, two novel state feedback controllers are designed according to state feedback control technique. In particular, based on the fractional Lyapunov stability theory, the finite-time stability theory and Young inequality, some novel algebraic synchronization criteria are obtained to ensure the finite-time synchronization of a class of drive-response fractional-order memristive recurrent neural networks with discontinuous activation functions. Moreover, we give the estimation of the upper bound of the settling time for synchronization. Finally, a simulation example is given to show the effectiveness of our theoretical results.