Fixed-time synchronization of delayed BAM neural networks via new fixed-time stability results and non-chattering quantized controls

Abstract

In this paper, in order to obtain a smaller estimation of settling time, reduce chattering caused by sign function and improve network communication efficiency, the fixed-time (FXT) synchronization of delayed BAM neural networks is analyzed based on some new FXT stability results and non-chattering quantized controllers. Firstly, by comprehensively discussing the conditions of power laws in differential inequalities, a new FXT stability lemma is presented and a smaller upper bound of settling time is estimated. Then, unlike previous controllers with sign functions, a non-chattering quantized state feedback control and a non-chattering quantized pinning control are designed, and some sufficient conditions are derived to ensure FXT synchronization of the established system. Finally, two numerical simulations are given to verify the effectiveness of the theoretical results. The results show that compared with the previous researches, this paper provides a smaller upper bound. However, the convergence time of the uncontrolled nodes is indirectly affected by the coupling of the controlled nodes and is much longer than the estimated upper bound.