The purpose of this paper is to investigate the exponential stability for discrete-time homogeneous impulsive positive delay systems of degree one. By virtue of max-separable Lyapunov functions together with Razumikhin technique, both the stability results that impulses act as stabilizers and the stability results that impulses act as perturbations are obtained. It should be noted that it is the first time that impulsive exponential stabilization results and Razumikhin type exponential stability results for discrete-time homogeneous impulsive positive delay systems of degree one are given. Two numerical examples are provided to show the effectiveness of the proposed results.

本文的目的是研究一阶离散时间齐次脉冲正时滞系统的指数稳定性。通过最大可分的Lyapunov函数和Razumikhin技术，既获得了将脉冲用作稳定器的稳定性结果，又获得了将脉冲用作微扰的稳定性结果。应当指出，这是第一次给出离散度为一阶的齐次脉冲正时滞系统的脉冲指数稳定结果和Razumikhin型指数稳定性结果。提供了两个数值示例来说明所提出的结果的有效性。