{"title":"Finite-Time Stability and Instability of Nonlinear Impulsive Systems","authors":"Guihua Zhao null, Hui Liang","doi":"10.4208/aamm.oa-2021-0381","DOIUrl":null,"url":null,"abstract":". In this paper, the finite-time stability and instability are studied for nonlinear impulsive systems. There are mainly four concerns. 1) For the system with stabilizing impulses, a Lyapunov theorem on global finite-time stability is presented. 2) When the system without impulsive effects is globally finite-time stable (GFTS) and the settling time is continuous at the origin, it is proved that it is still GFTS over any class of impulse sequences, if the mixed impulsive jumps satisfy some mild conditions. 3) For systems with destabilizing impulses, it is shown that to be finite-time stable, the destabilizing impulses should not occur too frequently, otherwise, the origin of the impulsive system is finite-time instable, which are formulated by average dwell time (ADT) conditions respectively. 4) A theorem on finite-time instability is provided for system with stabilizing impulses. For each GFTS theorem of impulsive systems con-sidered in this paper, the upper boundedness of settling time is given, which depends on the initial value and impulsive effects. Some numerical examples are given to illus-trate the theoretical analysis.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics and Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/aamm.oa-2021-0381","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
. In this paper, the finite-time stability and instability are studied for nonlinear impulsive systems. There are mainly four concerns. 1) For the system with stabilizing impulses, a Lyapunov theorem on global finite-time stability is presented. 2) When the system without impulsive effects is globally finite-time stable (GFTS) and the settling time is continuous at the origin, it is proved that it is still GFTS over any class of impulse sequences, if the mixed impulsive jumps satisfy some mild conditions. 3) For systems with destabilizing impulses, it is shown that to be finite-time stable, the destabilizing impulses should not occur too frequently, otherwise, the origin of the impulsive system is finite-time instable, which are formulated by average dwell time (ADT) conditions respectively. 4) A theorem on finite-time instability is provided for system with stabilizing impulses. For each GFTS theorem of impulsive systems con-sidered in this paper, the upper boundedness of settling time is given, which depends on the initial value and impulsive effects. Some numerical examples are given to illus-trate the theoretical analysis.
期刊介绍:
Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.