{"title":"具有一般时变时滞的超线性混合随机系统的改进时滞相关稳定性","authors":"Henglei Xu, Xuerong Mao","doi":"10.1016/j.nahs.2023.101413","DOIUrl":null,"url":null,"abstract":"<div><p>In the recent paper (Fei et al., 2019), the study of delay-dependent stability of hybrid stochastic differential delay equations (SDDEs) was generalized to superlinear ones (namely, do not satisfy the usual linear growth condition). However, the theory developed there could not be applied to hybrid SDDEs with non-differentiable time delays, or whose drift coefficients miss the key decomposition in (Fei et al., 2019) (see Assumption 1 below). This paper therefore is to deal with these two challenging problems so that the delay-dependent stability criteria derived in (Fei et al., 2019) could be improved. The decomposition scheme is modified in order to include more general hybrid SDDEs. The differentiability assumption on time-varying delays is replaced by a relatively weaker one. Also the Lyapunov functional used in this paper is modulated to adapt to these new changes. Finally, two interesting examples, an application to mosquito model, and design of nonlinear delay feedback control, respectively, are given to demonstrate the effectiveness of our new theory.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Improved delay-dependent stability of superlinear hybrid stochastic systems with general time-varying delays\",\"authors\":\"Henglei Xu, Xuerong Mao\",\"doi\":\"10.1016/j.nahs.2023.101413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the recent paper (Fei et al., 2019), the study of delay-dependent stability of hybrid stochastic differential delay equations (SDDEs) was generalized to superlinear ones (namely, do not satisfy the usual linear growth condition). However, the theory developed there could not be applied to hybrid SDDEs with non-differentiable time delays, or whose drift coefficients miss the key decomposition in (Fei et al., 2019) (see Assumption 1 below). This paper therefore is to deal with these two challenging problems so that the delay-dependent stability criteria derived in (Fei et al., 2019) could be improved. The decomposition scheme is modified in order to include more general hybrid SDDEs. The differentiability assumption on time-varying delays is replaced by a relatively weaker one. Also the Lyapunov functional used in this paper is modulated to adapt to these new changes. Finally, two interesting examples, an application to mosquito model, and design of nonlinear delay feedback control, respectively, are given to demonstrate the effectiveness of our new theory.</p></div>\",\"PeriodicalId\":49011,\"journal\":{\"name\":\"Nonlinear Analysis-Hybrid Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2023-08-22\",\"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/S1751570X23000845\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Hybrid Systems","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1751570X23000845","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
摘要
在最近的论文(Fei et al.,2019)中,将混合随机微分时滞方程(SDDE)的时滞相关稳定性研究推广到超线性方程(即不满足通常的线性增长条件)。然而,在那里发展的理论不能应用于具有不可微时延的混合SDDE,或者其漂移系数错过了(Fei et al.,2019)中的关键分解(见下文假设1)。因此,本文将处理这两个具有挑战性的问题,以便改进(Fei et al.,2019)中导出的延迟相关稳定性准则。为了包括更通用的混合SDDE,对分解方案进行了修改。时变时滞的可微性假设被一个相对较弱的假设所取代。此外,本文中使用的李雅普诺夫函数也被调制以适应这些新的变化。最后,给出了两个有趣的例子,分别应用于蚊式模型和非线性延迟反馈控制的设计,以证明我们新理论的有效性。
Improved delay-dependent stability of superlinear hybrid stochastic systems with general time-varying delays
In the recent paper (Fei et al., 2019), the study of delay-dependent stability of hybrid stochastic differential delay equations (SDDEs) was generalized to superlinear ones (namely, do not satisfy the usual linear growth condition). However, the theory developed there could not be applied to hybrid SDDEs with non-differentiable time delays, or whose drift coefficients miss the key decomposition in (Fei et al., 2019) (see Assumption 1 below). This paper therefore is to deal with these two challenging problems so that the delay-dependent stability criteria derived in (Fei et al., 2019) could be improved. The decomposition scheme is modified in order to include more general hybrid SDDEs. The differentiability assumption on time-varying delays is replaced by a relatively weaker one. Also the Lyapunov functional used in this paper is modulated to adapt to these new changes. Finally, two interesting examples, an application to mosquito model, and design of nonlinear delay feedback control, respectively, are given to demonstrate the effectiveness of our new theory.
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.