Tradeoff analysis between time cost and energy cost for fixed-time synchronization of discontinuous neural networks

This article focuses on the tradeoff analysis between time and energy costs for fixed -time synchronization (FXTS) of discontinuous neural networks (DNNs) with time -varying delays and mismatched parameters. First, a more comprehensive lemma is systematically established to study fixed -time stability, which is less conservative than those in most current results. Besides, theoretical proof has proven that the upper bounds of the settling time (ST) in this article are more accurate compared to existing results. Second, on the grounds of the new fixed -time stability lemma, fixed -time synchronization problem for discontinuous neural networks with timevarying delays and mismatched parameters is explored, and sufficient conditions for fixed -time synchronization are obtained. Further, the upper bounds of energy cost during the synchronization process are estimated. Third, in order to achieve a balance between time cost and energy cost, the genetic algorithm is utilized to find the satisfactory control parameter. Finally, a numerical example is provided to verify the theoretical analysis's correctness and the control mechanism's feasibility.