{"title":"Improved admissibility analysis for T-S fuzzy Markovian jump singular systems with time-varying delays","authors":"Xingyue Liang, Shengyuan Xu","doi":"10.1016/j.fss.2024.109069","DOIUrl":null,"url":null,"abstract":"<div><p>This article researches the admissibility analysis problem for T-S fuzzy Markovian jump singular systems (MJSSs) with time-varying delays. First, based on the new state decomposition vectors, an extended Lyapunov-Krasovskii functional (LKF) is formulated, which allows that the involved matrices are not all positive definite. And, this LKF not only considers the state integral variable, but also makes full use of the time derivative information of membership function, which undoubtedly provides an advantage to the results. Then, based on free matrix integral inequality, a modified version is derived to estimate the value of integral term generated during the derivation of LKF. Based on extended LKF and modified integral inequality, the admissibility criterion with less conservative is obtained for T-S fuzzy MJSSs. Finally, two simulation examples are offered to demonstrate the effectiveness of proposed method.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016501142400215X","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
This article researches the admissibility analysis problem for T-S fuzzy Markovian jump singular systems (MJSSs) with time-varying delays. First, based on the new state decomposition vectors, an extended Lyapunov-Krasovskii functional (LKF) is formulated, which allows that the involved matrices are not all positive definite. And, this LKF not only considers the state integral variable, but also makes full use of the time derivative information of membership function, which undoubtedly provides an advantage to the results. Then, based on free matrix integral inequality, a modified version is derived to estimate the value of integral term generated during the derivation of LKF. Based on extended LKF and modified integral inequality, the admissibility criterion with less conservative is obtained for T-S fuzzy MJSSs. Finally, two simulation examples are offered to demonstrate the effectiveness of proposed method.
期刊介绍：
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.
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