Stability analysis in continuous and discrete time, using the Cayley transform

N.C. Besseling; Heiko J. Zwart

doi:10.1007/s00020-010-1805-8

Stability analysis in continuous and discrete time, using the Cayley transform

N.C. Besseling, Heiko J. Zwart

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

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Abstract

For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman distance. This is extended to a class of Desch–Schappacher perturbations.

Original language	Undefined
Pages (from-to)	487-502
Number of pages	16
Journal	Integral equations and operator theory
Volume	68
Issue number	4
DOIs	https://doi.org/10.1007/s00020-010-1805-8
Publication status	Published - 2010

Keywords

EWI-19033
MSC-47D60
Discrete time
Stability
$C_0$-semigroups
IR-75125
Cayley transform
Continuous time
METIS-275758

Access to Document

10.1007/s00020-010-1805-8

Cite this

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title = "Stability analysis in continuous and discrete time, using the Cayley transform",

abstract = "For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman distance. This is extended to a class of Desch–Schappacher perturbations.",

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T1 - Stability analysis in continuous and discrete time, using the Cayley transform

AU - Besseling, N.C.

AU - Zwart, Heiko J.

N1 - Open Access

PY - 2010

Y1 - 2010

N2 - For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman distance. This is extended to a class of Desch–Schappacher perturbations.

AB - For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman distance. This is extended to a class of Desch–Schappacher perturbations.

KW - EWI-19033

KW - MSC-47D60

KW - Discrete time

KW - Stability

KW - $C_0$-semigroups

KW - IR-75125

KW - Cayley transform

KW - Continuous time

KW - METIS-275758

U2 - 10.1007/s00020-010-1805-8

DO - 10.1007/s00020-010-1805-8

M3 - Article

VL - 68

SP - 487

EP - 502

JO - Integral equations and operator theory

JF - Integral equations and operator theory

SN - 0378-620X

IS - 4

ER -