Aouragh, M.D. (2016) Uniform stabilization of a hybrid system of elasticity: Riesz basis approach. In: UNSPECIFIED.

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Official URL: https://www.scopus.com/inward/record.uri?eid=2-s2....

Abstract

A hybrid system, composed of an elastic beam governed by an Euler- Bernoulli beam equation and a linked rigid body governed by an ordinary differential equation, is considered. This paper studies the basis property and the stability of a hybrid system when the usual linear boundary feedback is applied to the end without mass. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. As consequence expressions of eigenvalues, the spectrum-determined growth condition and the exponential stability are readily presented. To confirm numerically the asymptotic estimate of eigenvalues, we shall use the spectral method to calculate the eigenvalues. © Springer International Publishing Switzerland 2016.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Uncontrolled Keywords: Continuum mechanics; Difference equations; Differential equations; Feedback; Hybrid systems; Ordinary differential equations; Stabilization, Asymptotic estimates; Beams; Boundary feedback; Euler-Bernoulli beam equation; Riesz basis; Spectral methods; Spectrum; Spectrum-determined- growth conditions, Eigenvalues and eigenfunctions
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48
URI: http://eprints.umi.ac.ma/id/eprint/4003

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