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Stabilization of nonuniform Euler-Bernoulli beam with locally distributed feedbacks

Stabilization of nonuniform Euler-Bernoulli beam with locally distributed feedbacks In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Stabilization of nonuniform Euler-Bernoulli beam with locally distributed feedbacks

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0129-7
Publisher site
See Article on Publisher Site

Abstract

In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Dec 13, 2011

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