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Exponential stability of Timoshenko beam systemwith delay terms in boundary feedbacks*

Published online by Cambridge University Press:  31 March 2010

Zhong-Jie Han  and
Gen-Qi Xu
Zhong-Jie Han
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China. zjhan@tju.edu.cn
Gen-Qi Xu
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China. zjhan@tju.edu.cn
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Abstract


In this paper, the stability of a Timoshenko beam with time delaysin the boundary input is studied. The system is fixed at the leftend, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system iswell-posed. By the complete spectral analysis, we show that there isa sequence of eigenvectors and generalized eigenvectors of thesystem operator that forms a Riesz basis for the state Hilbert space. Hence the system satisfies the spectrum determined growth condition. Then we conclude the exponential stability of the system under certain conditions. Finally, we give some simulations to support our results.


Keywords

Timoshenko beamexponential stabilitytime delayRiesz basisfeedback control
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 2 , April 2011 , pp. 552 - 574
Copyright
© EDP Sciences, SMAI, 2010

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