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Robustness of polynomial stability with respect to unbounded perturbations

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Robustness of polynomial stability with respect to unbounded perturbations. / Paunonen, Lassi.

In: Systems and Control Letters, Vol. 62, No. 4, 2013, p. 331-337.

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Paunonen, Lassi. / Robustness of polynomial stability with respect to unbounded perturbations. In: Systems and Control Letters. 2013 ; Vol. 62, No. 4. pp. 331-337.

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@article{4a4ca85391ef420594d92cd276f02b8a,
title = "Robustness of polynomial stability with respect to unbounded perturbations",
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.",
author = "Lassi Paunonen",
note = "Contribution: organisation=mat,FACT1=1<br/>Portfolio EDEND: 2013-07-29<br/>Publisher name: Elsevier",
year = "2013",
doi = "10.1016/j.sysconle.2013.01.005",
language = "English",
volume = "62",
pages = "331--337",
journal = "Systems and Control Letters",
issn = "0167-6911",
publisher = "Elsevier",
number = "4",

}

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TY - JOUR

T1 - Robustness of polynomial stability with respect to unbounded perturbations

AU - Paunonen, Lassi

N1 - Contribution: organisation=mat,FACT1=1<br/>Portfolio EDEND: 2013-07-29<br/>Publisher name: Elsevier

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.

U2 - 10.1016/j.sysconle.2013.01.005

DO - 10.1016/j.sysconle.2013.01.005

M3 - Article

VL - 62

SP - 331

EP - 337

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 4

ER -