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

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

ESAIM: Control, Optimisation and Calculus of Variations (2005)

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

Abstract

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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.

How to cite

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Wang, 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 (2005): 12-34. <http://eudml.org/doc/90785>.

@article{Wang2005,
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. },
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.; exponential stability; exact controllability},
language = {eng},
month = {12},
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/90785},
volume = {12},
year = {2005},
}

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
DA - 2005/12//
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.; exponential stability; exact controllability
UR - http://eudml.org/doc/90785
ER -

References

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