{"title":"具有无界时滞的离散时变系统的稳定性与镇定","authors":"Yige Guo , Fei Wang , Yihan Guo , Xiang Xu","doi":"10.1016/j.jfranklin.2025.107890","DOIUrl":null,"url":null,"abstract":"<div><div>This study addresses the stability and stabilization of discrete-time time-varying systems subject to unbounded delays. First, novel extended Lyapunov stability theorems are established, which permit positive differences in Lyapunov functionals. Based on these results, two low gain control laws are designed for some discrete-time linear time-varying (LTV) systems subject to unbounded input delays, ensuring global exponential stability of the closed-loop systems. At last, the efficacy of the proposed control schemes is demonstrated by two numerical examples.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 13","pages":"Article 107890"},"PeriodicalIF":3.7000,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability and stabilization of discrete-time time-varying systems with unbounded delays\",\"authors\":\"Yige Guo , Fei Wang , Yihan Guo , Xiang Xu\",\"doi\":\"10.1016/j.jfranklin.2025.107890\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This study addresses the stability and stabilization of discrete-time time-varying systems subject to unbounded delays. First, novel extended Lyapunov stability theorems are established, which permit positive differences in Lyapunov functionals. Based on these results, two low gain control laws are designed for some discrete-time linear time-varying (LTV) systems subject to unbounded input delays, ensuring global exponential stability of the closed-loop systems. At last, the efficacy of the proposed control schemes is demonstrated by two numerical examples.</div></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":\"362 13\",\"pages\":\"Article 107890\"},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2025-07-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0016003225003837\",\"RegionNum\":3,\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003225003837","RegionNum":3,"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}
Stability and stabilization of discrete-time time-varying systems with unbounded delays
This study addresses the stability and stabilization of discrete-time time-varying systems subject to unbounded delays. First, novel extended Lyapunov stability theorems are established, which permit positive differences in Lyapunov functionals. Based on these results, two low gain control laws are designed for some discrete-time linear time-varying (LTV) systems subject to unbounded input delays, ensuring global exponential stability of the closed-loop systems. At last, the efficacy of the proposed control schemes is demonstrated by two numerical examples.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.