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

¹ Department of Mathematics, Beijing Institue of Technology, Beijing, 100081, P.R. China; wangjc@graduate.hku.hk
² School of Computational and Applied Mathematics, University of the Witwatersrand, Private 3, Wits 2050, Johannesburg, South Africa.
³ Institute of Systems Science, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P.R. China; bzguo@iss.ac.cn
⁴ Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36 Al Khodh 123, Muscat, Sultanate of Oman.

Received: 1 June 2004
Accepted: 3 February 2005

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.