Finite-time quantized synchronization of coupled discontinuous competitive neural networks with proportional delay and impulsive effects

Usually, it is very difficult to overcome the effects of time delay and impulse simultaneously in finite-time control area. The present paper solves this problem by considering finite-time synchronization (FTS) and control in an array of competitive neural networks (CNNs) with discontinuous activations, proportional delays, as well as impulsive effects. Since the proportional delays are unbounded and the discontinuous activations usually induce uncertain Filippov solutions, new analytical techniques have to be developed. Quantized control scheme is designed to reduce the control cost and save channel resources. By constructing new Lyapunov functionals and comparison system, several sufficient conditions are obtained to ensure that the coupled CNNs achieve synchronization in a finite settling time which is explicitly estimated. Finally, numerical simulations are provided to illustrate the effectiveness of theoretical analysis.