{"title":"Stability of Highly Nonlinear Stochastic Delay Systems with Hybrid Switchings","authors":"Yichi Liu, Quanxin Zhu","doi":"10.1007/s12346-024-01131-8","DOIUrl":null,"url":null,"abstract":"<p>Numerous studies have investigated the stability of highly nonlinear stochastic systems (HNSSs). However, previous works have primarily focused on either deterministic or random switchings. In this paper, we examine HNSSs with delays and two switching modes. First, we introduce a hybrid switching rule and construct a stopping time in segments, dividing the switching interval of the entire system into a deterministic switching interval and a stochastic switching interval. Second, we establish the existence and boundedness of the global solution of the system by using the Lyapunov function and the average dwell time method. Additionally, we prove the asymptotic stability and exponential stability of the system without relying on the linear growth condition (LGC). Finally, we provide an illustrative example to demonstrate the validity of the obtained results.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01131-8","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Numerous studies have investigated the stability of highly nonlinear stochastic systems (HNSSs). However, previous works have primarily focused on either deterministic or random switchings. In this paper, we examine HNSSs with delays and two switching modes. First, we introduce a hybrid switching rule and construct a stopping time in segments, dividing the switching interval of the entire system into a deterministic switching interval and a stochastic switching interval. Second, we establish the existence and boundedness of the global solution of the system by using the Lyapunov function and the average dwell time method. Additionally, we prove the asymptotic stability and exponential stability of the system without relying on the linear growth condition (LGC). Finally, we provide an illustrative example to demonstrate the validity of the obtained results.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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