International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 28, Pages 1807-1820
doi:10.1155/S0161171203011414
Riesz basis property of Timoshenko beams with boundary feedback control
De-Xing Feng1
, Gen-Qi Xu2
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
Abstract
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.