Fixed-Time Synchronization of Coupled Discontinuous Neural Networks with Nonidentical Perturbations

This paper investigates fixed-time synchronization of coupled neural networks with discontinuous activation functions and nonidentical perturbations under the framework of Filippov solution. In order to overcome uncertainties of the Filippov solution and the effects of nonidentical perturbations, 1-norm based techniques are developed. By designing new state feedback controllers, constructing new Lyapunov functional, and utilizing differential inclusion theory, several sufficient conditions are obtained to ensure that the coupled discontinuous neural networks (CDNNs) to be synchronized in a fixed settling time. Results of this paper improve corresponding ones which only finite-time synchronization can be achieved for CDNNs. Finally, numerical simulations are offered to verify the effectiveness of the theoretical analysis.