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.
@article{urn:eudml:doc:44470,
title = {Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {14},
year = {2001},
pages = {205-229},
zbl = {0985.35054},
mrnumber = {MR1851729},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44470}
}
Guo, Bao-Zhu; Chan, K. Y. Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control.. Revista Matemática de la Universidad Complutense de Madrid, Tome 14 (2001) pp. 205-229. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44470/