{"title":"使用采样控制器的延迟马尔可夫跃迁系统的稳定问题","authors":"","doi":"10.1016/j.jfranklin.2024.107194","DOIUrl":null,"url":null,"abstract":"<div><p>This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stabilization of delayed Markovian jump systems with sampled controllers\",\"authors\":\"\",\"doi\":\"10.1016/j.jfranklin.2024.107194\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.</p></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S001600322400615X\",\"RegionNum\":3,\"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":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S001600322400615X","RegionNum":3,"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}
Stabilization of delayed Markovian jump systems with sampled controllers
This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.