{"title":"具有Caputo分数导数的线性脉冲微分代数系统的能控性和可观测性","authors":"C. Tunç, A. Zehra, Awais Younas","doi":"10.22034/CMDE.2020.39372.1724","DOIUrl":null,"url":null,"abstract":"Linear impulsive fractional differential-algebraic systems (LIFDAS) in a finite-dimensional space are studied. We obtain the solution of LIFDAS. Using Gramian matrices, necessary and sufficient conditions for controllability and observability of time-varying LIFDAS are established. We acquired criterion for time-invariant LIFDAS in the form of rank conditions. The results are more generalized than the results that are obtained for various differential-algebraic systems without impulses","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative\",\"authors\":\"C. Tunç, A. Zehra, Awais Younas\",\"doi\":\"10.22034/CMDE.2020.39372.1724\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Linear impulsive fractional differential-algebraic systems (LIFDAS) in a finite-dimensional space are studied. We obtain the solution of LIFDAS. Using Gramian matrices, necessary and sufficient conditions for controllability and observability of time-varying LIFDAS are established. We acquired criterion for time-invariant LIFDAS in the form of rank conditions. The results are more generalized than the results that are obtained for various differential-algebraic systems without impulses\",\"PeriodicalId\":44352,\"journal\":{\"name\":\"Computational Methods for Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods for Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22034/CMDE.2020.39372.1724\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2020.39372.1724","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative
Linear impulsive fractional differential-algebraic systems (LIFDAS) in a finite-dimensional space are studied. We obtain the solution of LIFDAS. Using Gramian matrices, necessary and sufficient conditions for controllability and observability of time-varying LIFDAS are established. We acquired criterion for time-invariant LIFDAS in the form of rank conditions. The results are more generalized than the results that are obtained for various differential-algebraic systems without impulses
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