Full paper in PDF:
$%B.-Z. Guo and K.-Y. Chan, Riesz basis generation, Eigenvalues distribution, and exponential stability for a Euler-Bernouilli beam with joint feedback control, Rev. Mat. Complut. 14 (2001), no. 1, 205229.%$

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
Department of Mathematics

The University of Kong Kong — Hong Kong

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


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.