带有时滞脉冲的非线性随机系统的稳定性分析  

Stability analysis of nonlinear stochastic systems with delayed impulses

作　　者：谢本旺 姚凤麒 程培[2] XIE Ben-wang;YAO Feng-qi;CHENG Pei(School of Electrical and Information Engineering,Anhui University of Technology,Maanshan Anhui 243000,China;School of Mathematical Sciences,Anhui University,Hefei Anhui 230601,China)

机构地区：[1]安徽工业大学电气与信息工程学院,安徽马鞍山243000 [2]安徽大学数学科学学院,安徽合肥230601

出　　处：《控制理论与应用》2025年第3期563-568,共6页Control Theory & Applications

摘　　要：本文研究带有时滞脉冲效应的非线性随机微分系统的p阶矩指数稳定性和几乎指数稳定性问题.基于脉冲控制理论和平均脉冲间隔的思想,利用伊藤公式,得到了系统基于Lyapunov理论的p阶矩指数稳定和几乎指数稳定的充分条件.结果表明,时滞脉冲的存在除了破环系统的稳定性外,还可以用来镇定不稳定的连续系统.最后,通过数值例子说明了理论结果的有效性.In this paper,the p th moment exponential stability and almost exponential stability of nonlinear stochastic differential system with delayed impulsive effect are studied.On the foundation of the impulsive control theory and the idea of average impulsive interval,using the Itˆo formula,some sufficient conditions for the p th exponential stability and the almost exponential stability based on the Lyapunov theory are obtained.The results show that the existence of impulsive delay can not only destroy the stability of the system,but also be used to stabilize the unstable continuous dynamics.Finally,some numerical simulations are presented to illustrate our proposed results.

关 键 词：时滞脉冲 平均脉冲区间 p阶矩指数稳定 几乎指数稳定 

分 类 号：O17[理学—数学]