{"title":"基于加权相关Lyapunov函数的T-S模糊离散系统松弛稳定性判据","authors":"Wen-June Wang, Chung-Hsun Sun","doi":"10.1109/ICNSC.2005.1461175","DOIUrl":null,"url":null,"abstract":"A weighting dependent Lyapunov function based stability criterion for T-S fuzzy discrete systems has been studied in lots of literature. That is to find out r (number of rules) symmetric positive matrices P/sub iS/ to satisfy r/sup 2/ Lyapunov inequalities. The aim of this paper is to reduce the Lyapunov inequalities which should be satisfied with positive matrices P/sub iS/ then the conservatism of the stability conditions would be relaxed. From the viewpoint of the group of firing rules and the maximum distance between two successive states of the system, a new relaxed stability criterion based on the weighting dependent Lyapunov function is proposed. Finally, an example is illustrated to show the relaxation effectiveness of the proposed stability criterion.","PeriodicalId":313251,"journal":{"name":"Proceedings. 2005 IEEE Networking, Sensing and Control, 2005.","volume":"92 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"A weighting dependent Lyapunov function based relaxed stability criterion for T-S fuzzy discrete systems\",\"authors\":\"Wen-June Wang, Chung-Hsun Sun\",\"doi\":\"10.1109/ICNSC.2005.1461175\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A weighting dependent Lyapunov function based stability criterion for T-S fuzzy discrete systems has been studied in lots of literature. That is to find out r (number of rules) symmetric positive matrices P/sub iS/ to satisfy r/sup 2/ Lyapunov inequalities. The aim of this paper is to reduce the Lyapunov inequalities which should be satisfied with positive matrices P/sub iS/ then the conservatism of the stability conditions would be relaxed. From the viewpoint of the group of firing rules and the maximum distance between two successive states of the system, a new relaxed stability criterion based on the weighting dependent Lyapunov function is proposed. Finally, an example is illustrated to show the relaxation effectiveness of the proposed stability criterion.\",\"PeriodicalId\":313251,\"journal\":{\"name\":\"Proceedings. 2005 IEEE Networking, Sensing and Control, 2005.\",\"volume\":\"92 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings. 2005 IEEE Networking, Sensing and Control, 2005.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICNSC.2005.1461175\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. 2005 IEEE Networking, Sensing and Control, 2005.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICNSC.2005.1461175","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A weighting dependent Lyapunov function based relaxed stability criterion for T-S fuzzy discrete systems
A weighting dependent Lyapunov function based stability criterion for T-S fuzzy discrete systems has been studied in lots of literature. That is to find out r (number of rules) symmetric positive matrices P/sub iS/ to satisfy r/sup 2/ Lyapunov inequalities. The aim of this paper is to reduce the Lyapunov inequalities which should be satisfied with positive matrices P/sub iS/ then the conservatism of the stability conditions would be relaxed. From the viewpoint of the group of firing rules and the maximum distance between two successive states of the system, a new relaxed stability criterion based on the weighting dependent Lyapunov function is proposed. Finally, an example is illustrated to show the relaxation effectiveness of the proposed stability criterion.
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