{"title":"Stabilization of unstable impulsive systems via stochastic discrete-time feedback control with Lévy noise","authors":"Mengmeng Zhang, Quanxin Zhu","doi":"10.1016/j.nahs.2025.101585","DOIUrl":null,"url":null,"abstract":"<div><div>It is universally acknowledged that noise can stabilize systems. Given an unstable impulsive system, can it be stabilized by Lévy noise? In this article, we mainly discuss the stochastic stabilization of unstable impulsive systems via Lévy noise. First, the conditions for <span><math><mi>p</mi></math></span>-moment exponential stability of unstable impulsive systems under continuous-time feedback control with Lévy noise are derived using the Lyapunov function method. Second, the almost sure exponentially stable conditions for the unstable impulsive systems under discrete-time feedback control with Lévy noise are derived through the comparison method. Additionally, several new stochastic stabilization strategies are proposed to design stochastic discrete-time feedback control for deriving almost sure exponentially stable results through stochastic analysis. Finally, two examples and their relevant simulation figures are given to check the validity of the results.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"56 ","pages":"Article 101585"},"PeriodicalIF":3.7000,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Hybrid Systems","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1751570X25000111","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
It is universally acknowledged that noise can stabilize systems. Given an unstable impulsive system, can it be stabilized by Lévy noise? In this article, we mainly discuss the stochastic stabilization of unstable impulsive systems via Lévy noise. First, the conditions for -moment exponential stability of unstable impulsive systems under continuous-time feedback control with Lévy noise are derived using the Lyapunov function method. Second, the almost sure exponentially stable conditions for the unstable impulsive systems under discrete-time feedback control with Lévy noise are derived through the comparison method. Additionally, several new stochastic stabilization strategies are proposed to design stochastic discrete-time feedback control for deriving almost sure exponentially stable results through stochastic analysis. Finally, two examples and their relevant simulation figures are given to check the validity of the results.
期刊介绍：
Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.
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