Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.

Bao-Zhu Guo; K. Y. Chan

Revista Matemática Complutense (2001)

  • Volume: 14, Issue: 1, page 205-229
  • ISSN: 1139-1138

Abstract

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Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation with joint linear feedback control form a Riesz basis for the state space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation.

How to cite

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Guo, Bao-Zhu, and Chan, K. Y.. "Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.." Revista Matemática Complutense 14.1 (2001): 205-229. <http://eudml.org/doc/44470>.

@article{Guo2001,
abstract = {Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation with joint linear feedback control form a Riesz basis for the state space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation.},
author = {Guo, Bao-Zhu, Chan, K. Y.},
journal = {Revista Matemática Complutense},
keywords = {Autovalores; Espacios de Hilbert; Autofunciones; Estabilidad; Sistemas de control; Realimentación; spectrum-determined growth condition; asymptotic expansion},
language = {eng},
number = {1},
pages = {205-229},
title = {Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.},
url = {http://eudml.org/doc/44470},
volume = {14},
year = {2001},
}

TY - JOUR
AU - Guo, Bao-Zhu
AU - Chan, K. Y.
TI - Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.
JO - Revista Matemática Complutense
PY - 2001
VL - 14
IS - 1
SP - 205
EP - 229
AB - Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation with joint linear feedback control form a Riesz basis for the state space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation.
LA - eng
KW - Autovalores; Espacios de Hilbert; Autofunciones; Estabilidad; Sistemas de control; Realimentación; spectrum-determined growth condition; asymptotic expansion
UR - http://eudml.org/doc/44470
ER -

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