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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
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 a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as well as the exact controllability are also addressed.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2006

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