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IMA Journal of Mathematical Control and Information 2001 18(2):241-251; doi:10.1093/imamci/18.2.241
© 2001 by Institute of Mathematics and its Applications
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The Riesz basis property of discrete operators and application to a Euler–Bernoulli beam equation with boundary linear feedback control

Bao-Zhu Guo1 and Runyi Yu2

1 Institute of Systems Science, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, People's Republic of China 2 Department of Electrical and Electronic Engineering, Eastern Mediterranean University, Gazimagusa, Mersin-10 Turkey

In this paper, we give an abstract condition of Riesz basis generation for discrete operators in Hilbert spaces, from which we show that the generalized eigenfunctions of a Euler–Bernoulli beam equation with boundary linear feedback control form a Riesz basis for the state Hilbert space. As an consequence, the asymptotic expression of eigenvalues together with exponential stability are readily presented.

Keywords: discrete operator; Riesz basis; spectrum-; determined growth condition.


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