Full paper in PDF:
$%B.-Z. Guo and K.-Y. Chan, Riesz basis generation, Eigenvalues distribution, and exponential stability for a Euler-Bernouilli beam with joint feedback control, Rev. Mat. Complut. 14 (2001), no. 1, 205–229.%$

Riesz Basis Generation, Eigenvalues Distribution, and Exponential Stability for a Euler-Bernouilli Beam with Joint Feedback Control
Bao-Zhu GUO and Kai-Yuen CHAN
Institute of Systems Science
Academy of Mathematics and System Sciences
Academia Sinica
Beijing 100081 — China
bzguo@isso3.iss.ac.cn
Department of Mathematics

The University of Kong Kong — Hong Kong

Received: June 9, 2000
Revised: July 19, 2000

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-Bernouilli 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.

2000 Mathematics Subject Classification: 35P20, 93D15.