Robust synchronisation control of discontinuous CGNNs with time-varying delays

Abstract

Fixed-time synchronisation requires that the settling time is independent of the initial synchronisation errors and the upper bound of the settling time can be given in advance. From this point of view, the fixed time synchronisation is more favourable and applicable. This paper aims to investigate the fixed-time synchronisation and fixed-time anti-synchronisation of Cohen-Grossberg master-slave neural networks with discontinuous neuron activations and time delays. For the purpose of fixed-time synchronisation, under the framework of Filippov solution, by using the Lyapunov-Krasovskii functional approach and designing a novel discontinuous feedback control procedure for the slave neural networks, some sufficient criteria are firstly derived to design the control parameters for achieving synchronisation within a fixed time for the proposed discontinuous Cohen-Grossberg neural networks. Then, based on the fixed-time synchronisation, another new discontinuous feedback controller is also designed to accomplish the fixed-time anti-synchronisation for the considered neural system. Finally, two numerical examples associated with main theorems and corollaries are presented to illustrate the proposed methodologies.