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

Jun-Min Wang; Bao-Zhu Guo; Boumediène Chentouf^{[1]}

- [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 (2006)

- Volume: 12, Issue: 1, page 12-34
- ISSN: 1292-8119

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topWang, Jun-Min, Guo, Bao-Zhu, and Chentouf, Boumediène. "Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach." ESAIM: Control, Optimisation and Calculus of Variations 12.1 (2006): 12-34. <http://eudml.org/doc/245761>.

@article{Wang2006,

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.},

affiliation = {Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36 Al Khodh 123, Muscat, Sultanate of Oman.},

author = {Wang, Jun-Min, Guo, Bao-Zhu, Chentouf, Boumediène},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Riesz basis; sandwich beam; exponential stability; exact controllability},

language = {eng},

number = {1},

pages = {12-34},

publisher = {EDP-Sciences},

title = {Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach},

url = {http://eudml.org/doc/245761},

volume = {12},

year = {2006},

}

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

PB - EDP-Sciences

VL - 12

IS - 1

SP - 12

EP - 34

AB - 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.

LA - eng

KW - Riesz basis; sandwich beam; exponential stability; exact controllability

UR - http://eudml.org/doc/245761

ER -

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