Finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays

Abstract

This paper is concerned with the issue of the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays. For synchronizing the drive-response memristive neural networks in finite time, an adaptive state-feedback controller and a state-feedback controller are proposed, respectively. Then by using the theories of differential inclusions and set-valued map, the synchronization issue of drive-response memristive neural networks with discontinuous activation functions and mixed time-varying delays is transformed into the stabilization issue of the error system. Moreover, based on the stability theory, Forti Lemma and Hardy inequality, some novel algebraic synchronization criteria are deduced to ensure the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays under the adaptive state-feedback controller and the state-feedback controller. And the settling times for finite-time adaptive synchronization and finite-time synchronization are given. Furthermore, it is hard to estimate the initial conditions for a large system, so the settling times in this paper are not dependent on initial conditions of system. Finally, an example is provided to demonstrate the effectiveness of the obtained results.