时滞不确定差分方程的指数稳定性Exponential Stability of Uncertain Difference Equations with Time-Delays
李雅,卢琴云
摘要(Abstract)：
在现实世界的系统建模中，不确定性是一个不可忽视的因素。不确定差分方程作为描述离散不确定系统的有效工具，被广泛应用于控制系统建模中。时滞现象也广泛存在于实际系统中，其往往是导致系统性能下降甚至失稳的关键因素。文章针对一类带有时滞的不确定差分方程，提出了其p阶矩指数稳定性的定义，并基于Lyapunov直接法和Halanay不等式，建立了相应的稳定性判别准则。为了进一步提升理论结果的实用性，文章结合方程的α-路以及不确定变量的广义期望，对稳定性条件进行了简化处理。最后，通过数值仿真验证了所提方法的有效性，为时滞不确定系统的稳定性分析提供了一种新的理论支持。
关键词(KeyWords)： 不确定差分方程;指数稳定性;Lyapunov直接法;时滞
基金项目(Foundation): 安徽省高校科研计划项目（2023AH050513,2023AH050478）
作者(Author): 李雅,卢琴云
DOI: 10.13757/j.cnki.cn34-1328/n.2025.03.002
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