{"title":"Stability and stabilization of discrete-time linear time-varying systems via Lyapunov difference equations and inequalities","authors":"Jiacheng Dong, Bin Zhou","doi":"10.1016/j.sysconle.2025.106203","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the stability and stabilization issues of discrete-time linear time-varying (DLTV) systems are investigated. The recently proposed concepts of stability for continuous linear time-varying (LTV) systems are extended to DLTV systems, including uniform upper boundedness (by an exponential function) and uniform lower boundedness (by an exponential function). For the newly proposed concepts of stability, techniques for testing stability are developed. First, utilizing the scalar stable function, the Lyapunov difference inequalities (LDIs) provide both sufficient and necessary conditions for the new concepts of stability. Second, sufficient and necessary criteria based on Lyapunov difference equations are presented. Third, by introducing uniform complete controllability and uniform complete reconstructibility, the Lyapunov equations whose matrix Q is degenerated are further examined. Finally, a method for designing state feedback controller is presented.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"204 ","pages":"Article 106203"},"PeriodicalIF":2.5000,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125001859","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the stability and stabilization issues of discrete-time linear time-varying (DLTV) systems are investigated. The recently proposed concepts of stability for continuous linear time-varying (LTV) systems are extended to DLTV systems, including uniform upper boundedness (by an exponential function) and uniform lower boundedness (by an exponential function). For the newly proposed concepts of stability, techniques for testing stability are developed. First, utilizing the scalar stable function, the Lyapunov difference inequalities (LDIs) provide both sufficient and necessary conditions for the new concepts of stability. Second, sufficient and necessary criteria based on Lyapunov difference equations are presented. Third, by introducing uniform complete controllability and uniform complete reconstructibility, the Lyapunov equations whose matrix Q is degenerated are further examined. Finally, a method for designing state feedback controller is presented.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.