Stability of perturbed linear distributed parameter systems

L. Pandolfi; H. Zwart

doi:10.1016/0167-6911(91)90141-Z

Stability of perturbed linear distributed parameter systems

L. Pandolfi, H. Zwart

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Abstract

We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.

Original language	English
Pages (from-to)	257-264
Number of pages	8
Journal	Systems and control letters
Volume	17
Issue number	4
DOIs	https://doi.org/10.1016/0167-6911(91)90141-Z
Publication status	Published - 1991

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title = "Stability of perturbed linear distributed parameter systems",

abstract = "We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.",

author = "L. Pandolfi and H. Zwart",

year = "1991",

doi = "10.1016/0167-6911(91)90141-Z",

language = "English",

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pages = "257--264",

journal = "Systems and control letters",

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T1 - Stability of perturbed linear distributed parameter systems

AU - Pandolfi, L.

AU - Zwart, H.

PY - 1991

Y1 - 1991

N2 - We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.

AB - We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.

U2 - 10.1016/0167-6911(91)90141-Z

DO - 10.1016/0167-6911(91)90141-Z

M3 - Article

SN - 0167-6911

VL - 17

SP - 257

EP - 264

JO - Systems and control letters

JF - Systems and control letters

IS - 4

ER -

Stability of perturbed linear distributed parameter systems

Abstract

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