Basis property of a Rayleigh beam with boundary stabilization

Authors:
B. Z. Guo
Affiliations:
Professor, Institute of Systems Science, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, PRC
Venue:
Journal of Optimization Theory and Applications
Year:
2002

Citing 4
Cited 0

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Stability and Stabilization of Infinite Dimensional Systems with Applications

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Abstract

A Rayleigh beam equation with boundary stabilization control is considered. Using an abstract result on the Riesz basis generation of discrete operators in Hilbert spaces, we show that the closed-loop system is a Riesz spectral system; that is, there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis in the state Hilbert space. The spectrum-determined growth condition, distribution of eigenvalues, as well as stability of the system are developed. This paper generalizes the results in Ref. 1.