Finite-time Synchronization of Neural Networks with Multiple Proportional Delays via Non-chattering Control

Abstract

This paper investigates finite-time synchronization of neural networks (NNs) with multiple proportional delays. In order to cope with the difficulties induced by multiple proportional delays, suitable nonlinear variable transformations and new 1-norm-based analytical techniques are developed. By constructing Lyapunov functional and designing new designed controllers, several new sufficient conditions are derived to realize synchronization in finite time. Moreover, estimation of the upper bound of synchronization time is also provided for NNs with bounded delays or proportional delays. The designed controllers without sign function are simple, which means the chattering phenomenon in most of the existing results can be overcome. A numerical simulation is offered to verify the effectiveness of the theoretical analysis.