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IMA Journal of Mathematical Control and Information 2004 21(1):65-83; doi:10.1093/imamci/21.1.65
© 2004 by Institute of Mathematics and its Applications
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Riesz basis property of the generalized eigenvector system of a Timoshenko beam

Gen-Qi Xu1, De-Xing Feng2 and Siu Pang Yung3

1 Mathematics Department of Tianjin University, Tianjin, 300072, People's Republic of China 2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China 3 Department of Mathematics, University of Hong Kong, Hong Kong, People's Republic of China

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls applied to two ends is studied in this paper. The spectral property of the operator A determined by the closed loop system is investigated. It is shown that operator A has compact resolvent and generates a C<sub>0</sub> semigroup, and its spectrum consists of two branches and has two asymptotes under some conditions. Furthermore it is proved that the sequence of all generalized eigenvectors of the system principal operator forms a Riesz basis for the state Hilbert space.

Keywords: Timoshenko beam; boundary feedback; generalized eigenvector system; Riesz basis.

Received 22 April 2003. Revised


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