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Basis Property of a Rayleigh Beam with Boundary Stabilization

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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.

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Authors and Affiliations

  1. Academy of Mathematics and System Sciences, Academia Sinica, Institute of Systems Science, Beijing, PRC

    B.Z. Guo (Professor)

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  1. B.Z. Guo
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Guo, B. Basis Property of a Rayleigh Beam with Boundary Stabilization. Journal of Optimization Theory and Applications 112, 529–547 (2002). https://doi.org/10.1023/A:1017912031840

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  • DOI: https://doi.org/10.1023/A:1017912031840

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