Robustness of polynomial stability with respect to unbounded perturbations

Lassi Paunonen

doi:10.1016/j.sysconle.2013.01.005

Robustness of polynomial stability with respect to unbounded perturbations

Lassi Paunonen

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Abstract

In this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator. In addition, we also improve recent perturbation results for bounded finite rank perturbations. The results are illustrated with two examples. In the first one we consider the preservation of stability of a one-dimensional wave equation that has been stabilized polynomially with boundary feedback. In the second example we find conditions for the preservation of polynomial stability of a multiplication semigroup under unbounded rank one perturbations.

Translated title of the contribution	Robustness of polynomial stability with respect to unbounded perturbations
Original language	English
Pages (from-to)	331-337
Number of pages	7
Journal	Systems and Control Letters
Volume	62
Issue number	4
DOIs	https://doi.org/10.1016/j.sysconle.2013.01.005
Publication status	Published - 2013
Publication type	A1 Journal article-refereed

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10.1016/j.sysconle.2013.01.005

Paunonen robustness of polynomial stability
NOTICE: this is the author’s version of a work that was accepted for publication in Systems and Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Systems and Control Letters, vol. 62, issue 4 (April 2013), DOI 10.1016/j.sysconle.2013.01.005

http://urn.fi/URN:NBN:fi:tty-201312161488

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PY - 2013

Y1 - 2013

N2 - In this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator. In addition, we also improve recent perturbation results for bounded finite rank perturbations. The results are illustrated with two examples. In the first one we consider the preservation of stability of a one-dimensional wave equation that has been stabilized polynomially with boundary feedback. In the second example we find conditions for the preservation of polynomial stability of a multiplication semigroup under unbounded rank one perturbations.

AB - In this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator. In addition, we also improve recent perturbation results for bounded finite rank perturbations. The results are illustrated with two examples. In the first one we consider the preservation of stability of a one-dimensional wave equation that has been stabilized polynomially with boundary feedback. In the second example we find conditions for the preservation of polynomial stability of a multiplication semigroup under unbounded rank one perturbations.

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DO - 10.1016/j.sysconle.2013.01.005

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SP - 331

EP - 337

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 4

ER -

Robustness of polynomial stability with respect to unbounded perturbations

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