Geodesic
Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach
Wang, Jun-Min  ; Guo, Bao-Zhu  ; Chentouf, Boumediène1 
1 Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36 Al Khodh 123, Muscat, Sultanate of Oman.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 12-34

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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.

DOI : 10.1051/cocv:2005030
Classification : 93C20, 93D15, 35D10, 47B06
Keywords: Riesz basis, sandwich beam, exponential stability, exact controllability

Wang, Jun-Min  ; Guo, Bao-Zhu  ; Chentouf, Boumediène 1

1 Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36 Al Khodh 123, Muscat, Sultanate of Oman. 
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Wang, Jun-Min; Guo, Bao-Zhu; Chentouf, Boumediène. Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 12-34. doi: 10.1051/cocv:2005030

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