Journal Article

The Riesz basis property of discrete operators and application to a Euler–Bernoulli beam equation with boundary linear feedback control

Bao‐Zhu Guo and Runyi Yu

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 18, issue 2, pages 241-251
Published in print June 2001 | ISSN: 0265-0754
Published online June 2001 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/18.2.241
The Riesz basis property of discrete operators and application to a Euler–Bernoulli beam equation with boundary linear feedback control

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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

Journal Article.  0 words. 

Subjects: Mathematics

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