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On the dynamic behavior and stability of controlled connected Rayleighbeams under pointwise output feedback

Published online by Cambridge University Press:  18 January 2008

Bao-Zhu Guo ,
Jun-Min Wang  and
Cui-Lian Zhou
Bao-Zhu Guo
Affiliation:
Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080, P.R. China; bzguo@iss.ac.cn School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa.
Jun-Min Wang
Affiliation:
Corresponding author: Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China; wangjc@graduate.hku.hk
Cui-Lian Zhou
Affiliation:
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China.
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Abstract

We study the dynamic behavior and stability of two connectedRayleigh beams that are subject to, in addition to two sensors andtwo actuators applied at the joint point, one of the actuators alsospecially distributed along the beams. We show that with thedistributed control employed, there is a set of generalizedeigenfunctions of the closed-loop system, which forms a Riesz basiswith parenthesis for the state space. Then both thespectrum-determined growth condition and exponential stability areconcluded for the system. Moreover, we show that the exponentialstability is independent of the location of the joint. The range ofthe feedback gains that guarantee the system to be exponentiallystable is identified.

Keywords

Rayleigh beamcollocated controlspectral analysisexponential stability
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 3 , July 2008 , pp. 632 - 656
Copyright
© EDP Sciences, SMAI, 2008

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