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Stabilization of vibrating beam with a tip mass controlled by combined feedback forces
Li, SJ; Wang, YT; Liang, ZD; Yu, JY; Zhu, GT
2001-04-01
Source PublicationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN0022-247X
Volume256Issue:1Pages:13-38
AbstractA flexible structure consisting of a Euler-Bernoulli beam with a tip mass is considered. To stabilize this system we use a boundary control laws: -u(xxx)(l, t) + mu(tt)(l, t) = - alphau(t)(l, t) + betau(xxxt)(l, t) and u(xx)(l, t) = - gammau(xt)(l, t). A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. We prove that all of the generalized eigenfunctions of (2.9) form a Riesz basis of H By a new method, we prove that the operator A generates a C-0 contraction semigroup T(t), t greater than or equal to 0. Furthermore T(t), t greater than or equal to 0, is uniformly exponentially stable and the optimal exponential decay rate can be obtained from the spectrum of the system. (C) 2001 Academic Press.
Keywordbeam equation boundary feedback control Riesz basis exponential stabilization optimal exponential decay rate
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000167833300002
PublisherACADEMIC PRESS INC
Citation statistics
Cited Times:8[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/16301
Collection中国科学院数学与系统科学研究院
Affiliation1.Shanxi Univ, Dept Math, Taiyuan 030006, Peoples R China
2.Inst Informat & Control, Beijing 100037, Peoples R China
3.Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Li, SJ,Wang, YT,Liang, ZD,et al. Stabilization of vibrating beam with a tip mass controlled by combined feedback forces[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2001,256(1):13-38.
APA Li, SJ,Wang, YT,Liang, ZD,Yu, JY,&Zhu, GT.(2001).Stabilization of vibrating beam with a tip mass controlled by combined feedback forces.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,256(1),13-38.
MLA Li, SJ,et al."Stabilization of vibrating beam with a tip mass controlled by combined feedback forces".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 256.1(2001):13-38.
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