{"title":"Finite-time stability and stabilization of discrete-time hybrid systems","authors":"Qiyao Wang , Guoping Lu , Min Zhao , Jitao Sun","doi":"10.1016/j.sysconle.2024.105832","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with the finite-time stability and stabilization problems for a class of hybrid systems, which consists of discrete-time continuous-valued and Boolean dynamics. First, we introduce the so-called systems briefly and give the algebraic form of the systems via Khatri–Rao product and semi-tensor product (STP, i.e., Cheng product). Next, we originally propose the concept of finite-time stability (FTS) for the hybrid systems. Furthermore, some criteria of FTS for the hybrid systems are provided. Via a lemma we present, the computational complexity of the condition on FTS for the logical part could be reduced to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Based on these obtained results, two classes of controllers, state feedback controllers and logical controllers, are designed. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"189 ","pages":"Article 105832"},"PeriodicalIF":2.1000,"publicationDate":"2024-05-27","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/S0167691124001208","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
This paper is concerned with the finite-time stability and stabilization problems for a class of hybrid systems, which consists of discrete-time continuous-valued and Boolean dynamics. First, we introduce the so-called systems briefly and give the algebraic form of the systems via Khatri–Rao product and semi-tensor product (STP, i.e., Cheng product). Next, we originally propose the concept of finite-time stability (FTS) for the hybrid systems. Furthermore, some criteria of FTS for the hybrid systems are provided. Via a lemma we present, the computational complexity of the condition on FTS for the logical part could be reduced to . Based on these obtained results, two classes of controllers, state feedback controllers and logical controllers, are designed. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results.
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.
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