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An explicit Floquet-type representation of Riccati aperiodic exponential semigroups

hal.structure.identifierUniversity of Technology Sydney [UTS]
dc.contributor.authorBISHOP, Adrian
hal.structure.identifierCentre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDEL MORAL, Pierre
dc.date.accessioned2024-04-04T02:57:53Z
dc.date.available2024-04-04T02:57:53Z
dc.date.issued2019
dc.identifier.issn0020-7179
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192604
dc.description.abstractEnThe article presents a rather surprising Floquet-type representation of time-varying transition matri-ces associated with a class of nonlinear matrix differentialRiccati equations. The main difference withconventional Floquet theory comes from the fact that the underlying flow of the solution matrix is aperi-odic. The monodromy matrix associated with this Floquet representation coincides with the exponential(fundamental) matrix associated with the stabilizing fixedpoint of the Riccati equation. The second partof this article is dedicated to the application of this representation to the stability of matrix differentialRiccati equations. We provide refined global and local contraction inequalities for the Riccati exponentialsemigroup that depend linearly on the spectral norm of the initial condition. These refinements improveupon existing results and are a direct consequence of the Floquet-type representation, yielding whatseems to be the first results of this type for this class of models.
dc.language.isoen
dc.publisherTaylor & Francis
dc.title.enAn explicit Floquet-type representation of Riccati aperiodic exponential semigroups
dc.typeArticle de revue
dc.identifier.doi10.1080/00207179.2019.1590647
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.journalInternational Journal of Control
bordeaux.page1-9
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02429300
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02429300v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=International%20Journal%20of%20Control&rft.date=2019&rft.spage=1-9&rft.epage=1-9&rft.eissn=0020-7179&rft.issn=0020-7179&rft.au=BISHOP,%20Adrian&DEL%20MORAL,%20Pierre&rft.genre=article


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