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

Bao-Zhu Guo; Jun-Min Wang; Cui-Lian Zhou

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 3, page 632-656
  • ISSN: 1292-8119

Abstract

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We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability are concluded for the system. Moreover, we show that the exponential stability is independent of the location of the joint. The range of the feedback gains that guarantee the system to be exponentially stable is identified.

How to cite

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Guo, Bao-Zhu, Wang, Jun-Min, and Zhou, Cui-Lian. "On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2008): 632-656. <http://eudml.org/doc/250311>.

@article{Guo2008,
abstract = { We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability are concluded for the system. Moreover, we show that the exponential stability is independent of the location of the joint. The range of the feedback gains that guarantee the system to be exponentially stable is identified. },
author = {Guo, Bao-Zhu, Wang, Jun-Min, Zhou, Cui-Lian},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Rayleigh beam; collocated control; spectral analysis; exponential stability; exponential stability},
language = {eng},
month = {1},
number = {3},
pages = {632-656},
publisher = {EDP Sciences},
title = {On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback},
url = {http://eudml.org/doc/250311},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Guo, Bao-Zhu
AU - Wang, Jun-Min
AU - Zhou, Cui-Lian
TI - On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/1//
PB - EDP Sciences
VL - 14
IS - 3
SP - 632
EP - 656
AB - We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability are concluded for the system. Moreover, we show that the exponential stability is independent of the location of the joint. The range of the feedback gains that guarantee the system to be exponentially stable is identified.
LA - eng
KW - Rayleigh beam; collocated control; spectral analysis; exponential stability; exponential stability
UR - http://eudml.org/doc/250311
ER -

References

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