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.
Keywords: Riesz basis, sandwich beam, exponential stability, exact controllability
Wang, Jun-Min ; Guo, Bao-Zhu ; Chentouf, Boumediène 1
@article{COCV_2006__12_1_12_0,
author = {Wang, Jun-Min and Guo, Bao-Zhu and Chentouf, Boumedi\`ene},
title = {Boundary feedback stabilization of a three-layer sandwich beam : {Riesz} basis approach},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {12--34},
year = {2006},
publisher = {EDP Sciences},
volume = {12},
number = {1},
doi = {10.1051/cocv:2005030},
mrnumber = {2192066},
zbl = {1107.93031},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2005030/}
}
TY - JOUR AU - Wang, Jun-Min AU - Guo, Bao-Zhu AU - Chentouf, Boumediène TI - Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 12 EP - 34 VL - 12 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2005030/ DO - 10.1051/cocv:2005030 LA - en ID - COCV_2006__12_1_12_0 ER -
%0 Journal Article %A Wang, Jun-Min %A Guo, Bao-Zhu %A Chentouf, Boumediène %T Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 12-34 %V 12 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2005030/ %R 10.1051/cocv:2005030 %G en %F COCV_2006__12_1_12_0
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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