Continuity of the spectral factorization on a vertical strip

Birgit Jacob; Joseph Winkin; Hans Zwart

doi:10.1016/S0167-6911(99)00019-5

Continuity of the spectral factorization on a vertical strip

Birgit Jacob, Joseph Winkin, Hans Zwart

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

Résumé

The continuity of the mapping which associates a spectral factor to a spectral density is investigated. This mapping can be defined on several classes of spectral densities and spectral factors. For the usual largest class of spectral densities, i.e., essential bounded functions on the imaginary axis that are bounded away from zero, it is known that this mapping is not continuous. It is shown here that for slightly smaller, but still generic class the mapping becomes continuous.

langue originale	Anglais
Pages (de - à)	183-192
Nombre de pages	10
journal	Systems and Control Letters
Volume	37
Numéro de publication	4
Les DOIs	https://doi.org/10.1016/S0167-6911(99)00019-5
Etat de la publication	Publié - 26 juil. 1999

Financement

This work was supported by the Human Capital and Mobility European program (project No. CHRX-CT93-0402). The authors wish to thank George Weiss (Imperial College of London, UK) for some helpful discussions.

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10.1016/S0167-6911(99)00019-5

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title = "Continuity of the spectral factorization on a vertical strip",

abstract = "The continuity of the mapping which associates a spectral factor to a spectral density is investigated. This mapping can be defined on several classes of spectral densities and spectral factors. For the usual largest class of spectral densities, i.e., essential bounded functions on the imaginary axis that are bounded away from zero, it is known that this mapping is not continuous. It is shown here that for slightly smaller, but still generic class the mapping becomes continuous.",

keywords = "Approximate spectral factorization, Coercivity, Spectral density, Spectral factor",

author = "Birgit Jacob and Joseph Winkin and Hans Zwart",

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AU - Winkin, Joseph

AU - Zwart, Hans

PY - 1999/7/26

Y1 - 1999/7/26

N2 - The continuity of the mapping which associates a spectral factor to a spectral density is investigated. This mapping can be defined on several classes of spectral densities and spectral factors. For the usual largest class of spectral densities, i.e., essential bounded functions on the imaginary axis that are bounded away from zero, it is known that this mapping is not continuous. It is shown here that for slightly smaller, but still generic class the mapping becomes continuous.

AB - The continuity of the mapping which associates a spectral factor to a spectral density is investigated. This mapping can be defined on several classes of spectral densities and spectral factors. For the usual largest class of spectral densities, i.e., essential bounded functions on the imaginary axis that are bounded away from zero, it is known that this mapping is not continuous. It is shown here that for slightly smaller, but still generic class the mapping becomes continuous.

KW - Approximate spectral factorization

KW - Coercivity

KW - Spectral density

KW - Spectral factor

UR - https://www.scopus.com/pages/publications/0001548461

U2 - 10.1016/S0167-6911(99)00019-5

DO - 10.1016/S0167-6911(99)00019-5

M3 - Article

VL - 37

SP - 183

EP - 192

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 4

ER -

Continuity of the spectral factorization on a vertical strip

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