Potential Impacts of Delay on Stability of Impulsive Control Systems

控制理论(社会学) 理论(学习稳定性) 指数稳定性 脉冲(物理) 控制系统 群时延和相位时延 数学 计算机科学 控制(管理) 工程类 非线性系统 物理 带宽(计算) 计算机网络 量子力学 机器学习 人工智能 电气工程
作者
Jianquan Lu,Bangxin Jiang,Wei Xing Zheng
出处
期刊:IEEE Transactions on Automatic Control [Institute of Electrical and Electronics Engineers]
卷期号:67 (10): 5179-5190 被引量:74
标识
DOI:10.1109/tac.2021.3120672
摘要

In this article, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive time-delay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive systems, some potential impacts of delay on the stability are investigated. Particularly, the obtained results are extended to the case of impulsive control systems with hybrid impulses, which contain both stabilizing impulses and destabilizing impulses. Three illustrative examples are presented to reveal the potential impacts of delay on the stability of impulsive control systems.
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