International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 28, Pages 1807-1820

Riesz basis property of Timoshenko beams with boundary feedback control

De-Xing Feng,1 Gen-Qi Xu,2 and Siu-Pang Yung3

1Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
2Department of Mathematics, Shanxi University, Taiyuan 030006, China
3Department of Mathematics, Faculty of Science, University of Hong Kong (HKU), Hong Kong

Received 18 January 2001; Revised 28 June 2001

Copyright © 2003 De-Xing Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space.