Impulsive Stabilization of Nonautonomous Timescale-Type Neural Networks With Constant and Unbounded Time-Varying Delays

Abstract

This article focuses on the impulsive stabilization of nonautonomous timescale-type neural networks (NTNNs) with constant and unbounded time-varying delays. By choosing two discontinuous piecewise linear functions and employing the convex combination method, several algebraic criteria are demonstrated to achieve globally asymptotic stabilization of NTNNs with constant and unbounded time-varying delays. First, the asymptotic stability theorem for timescale-type systems is constructed by utilizing the timescale theory. Based on this asymptotic stability theorem, an impulsive control scheme is designed to guarantee global asymptotic stabilization of NTNNs with constant delay. Second, we propose several impulsive control schemes to achieve globally asymptotic stabilization of NTNNs with unbounded delay by virtue of the comparison strategy. Globally asymptotic stabilization criteria for NTNNs include the theoretical results of continuous-time neural networks (NNs), their discrete-time forms and NNs on continuous-discrete hybrid time scales. Especially, impulsive control for globally asymptotic stabilization of NTNNs with proportional delay is demonstrated without any variable transformation. Finally, the effectiveness of our proposed theoretical results is verified by four numerical examples.