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Boundary feedback stabilization of a three-layer sandwichbeam: Riesz basis approach

Published online by Cambridge University Press:  15 December 2005

Jun-Min Wang ,
Bao-Zhu Guo  and
Boumediène Chentouf
Jun-Min Wang
Affiliation:
Department of Mathematics, Beijing Institue of Technology, Beijing, 100081, P.R. China; wangjc@graduate.hku.hk School of Computational and Applied Mathematics, University of the Witwatersrand, Private 3, Wits 2050, Johannesburg, South Africa.
Bao-Zhu Guo
Affiliation:
School of Computational and Applied Mathematics, University of the Witwatersrand, Private 3, Wits 2050, Johannesburg, South Africa. Institute of Systems Science, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P.R. China; bzguo@iss.ac.cn
Boumediène Chentouf
Affiliation:
Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36 Al Khodh 123, Muscat, Sultanate of Oman.
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Abstract

In this paper, we consider the boundary stabilization of asandwich beam which consists of two outer stiff layers and acompliant middle layer. Using Riesz basis approach, we show thatthere is a sequence of generalized eigenfunctions, which forms aRiesz basis in the state space. As a consequence, thespectrum-determined growth condition as well as the exponentialstability of the closed-loop system are concluded. Finally, thewell-posedness and regularity in the sense of Salamon-Weiss classas well as the exact controllability are also addressed.

Keywords

Riesz basissandwich beamexponential stabilityexact controllability.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 1 , January 2006 , pp. 12 - 34
Copyright
© EDP Sciences, SMAI, 2006

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