Basis property of a Rayleigh beam with boundary stabilization

被引：11

作者：

Guo, BZ ^{[1
]}

机构：

[1] Acad Sinica, Acad Math & Syst Sci, Inst Syst Sci, Beijing, Peoples R China

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2002年 / 112卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Rayleigh beam; Riesz basis; spectrum-determined growth condition; stability;

D O I：

10.1023/A:1017912031840

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

A Rayleigh beam equation with boundary stabilization control is considered. Using an abstract result on the Riesz basis generation of discrete operators in Hilbert spaces, we show that the closed-loop system is a Riesz spectral system; that is, there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis in the state Hilbert space. The spectrum-determined growth condition, distribution of eigenvalues, as well as stability of the system are developed, This paper generalizes the results in Ref. 1.

引用

页码：529 / 547

页数：19

共 50 条

[1] Basis Property of a Rayleigh Beam with Boundary Stabilization
B.Z. Guo
Journal of Optimization Theory and Applications, 2002, 112 : 529 - 547
[2] A compact perturbation method for the boundary stabilization of the Rayleigh beam equation
Rao, B
APPLIED MATHEMATICS AND OPTIMIZATION, 1996, 33 (03): : 253 - 264
[3] The Riesz basis property of a Timoshenko beam with boundary feedback and application
Xu, GQ
Feng, DX
IMA JOURNAL OF APPLIED MATHEMATICS, 2002, 67 (04) : 357 - 370
[4] Spectral asymptotics, instability and Riesz basis property of root vectors for Rayleigh beam model with non-dissipative boundary conditions
Shubov, Marianna A.
ASYMPTOTIC ANALYSIS, 2014, 87 (3-4) : 147 - 190
[5] Basis property and stabilization of a translating tensioned beam through a pointwise control force
Guo, BZ
Xie, Y
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2004, 47 (8-9) : 1397 - 1409
[6] BOUNDARY STABILIZATION OF TIMOSHENKO BEAM
YAN Qingxu (Institute of Systems Science
SystemsScienceandMathematicalSciences, 2000, (04) : 376 - 384
[7] Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach
Wang, JM
Guo, BZ
Chentouf, B
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2006, 12 (01) : 12 - 34
[8] Exponential stabilization of a Rayleigh beam using collocated control
Weiss, George
Curtain, Ruth F.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (03) : 643 - 654
[9] STABILIZATION OF A RAYLEIGH BEAM WITH COLLOCATED PIEZOELECTRIC SENSOR/ACTUATOR
Bai, Yubo
Prieur, Christophe
Wang, Zhiqiang
EVOLUTION EQUATIONS AND CONTROL THEORY, 2024, 13 (01): : 67 - 97
[10] Boundary feedback stabilization of Timoshenko beam with boundary dissipation
Feng, DX
Shi, DH
Zhang, WT
SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1998, 41 (05): : 483 - 490

← 1 2 3 4 5 →