{"title":"区间时变时滞离散系统的时滞分布相关稳定性判据","authors":"Nan Xiao, Y. Jia, F. Matsuno","doi":"10.1109/ACC.2013.6580086","DOIUrl":null,"url":null,"abstract":"This paper studies the stability problem for discrete-time systems with interval time-varying delay. By dividing delay interval into two subintervals, a delay-dependent exponential stability criterion is obtained based on Lyapunov stability theory and reciprocally convex lemma. Furthermore, by assuming that the distribution of time-varying delay is known, the difference of Lyapunov functional is allowed to have positive upper bound for the value of time-varying delay in one subinterval, and a new delay distribution dependent stability criterion is obtained. The obtained result is also extended to cope with the robust delay distribution dependent stability problem for uncertain time-varying delay systems. All the obtained criteria are presented in terms of Linear Matrix Inequalities (LMIs). Finally one numerical example is given to show the effectiveness of the proposed method.","PeriodicalId":145065,"journal":{"name":"2013 American Control Conference","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Delay distribution dependent stability criteria for discrete-time systems with interval time-varying delay\",\"authors\":\"Nan Xiao, Y. Jia, F. Matsuno\",\"doi\":\"10.1109/ACC.2013.6580086\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies the stability problem for discrete-time systems with interval time-varying delay. By dividing delay interval into two subintervals, a delay-dependent exponential stability criterion is obtained based on Lyapunov stability theory and reciprocally convex lemma. Furthermore, by assuming that the distribution of time-varying delay is known, the difference of Lyapunov functional is allowed to have positive upper bound for the value of time-varying delay in one subinterval, and a new delay distribution dependent stability criterion is obtained. The obtained result is also extended to cope with the robust delay distribution dependent stability problem for uncertain time-varying delay systems. All the obtained criteria are presented in terms of Linear Matrix Inequalities (LMIs). Finally one numerical example is given to show the effectiveness of the proposed method.\",\"PeriodicalId\":145065,\"journal\":{\"name\":\"2013 American Control Conference\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2013 American Control Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ACC.2013.6580086\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 American Control Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.2013.6580086","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Delay distribution dependent stability criteria for discrete-time systems with interval time-varying delay
This paper studies the stability problem for discrete-time systems with interval time-varying delay. By dividing delay interval into two subintervals, a delay-dependent exponential stability criterion is obtained based on Lyapunov stability theory and reciprocally convex lemma. Furthermore, by assuming that the distribution of time-varying delay is known, the difference of Lyapunov functional is allowed to have positive upper bound for the value of time-varying delay in one subinterval, and a new delay distribution dependent stability criterion is obtained. The obtained result is also extended to cope with the robust delay distribution dependent stability problem for uncertain time-varying delay systems. All the obtained criteria are presented in terms of Linear Matrix Inequalities (LMIs). Finally one numerical example is given to show the effectiveness of the proposed method.