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

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

ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 12-34.

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.

Classification : 93C20, 93D15, 35D10, 47B06
Mots clés : Riesz basis, sandwich beam, exponential stability, exact controllability

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