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Weighted Admissibility and Wellposedness of Linear Systems in Banach Spaces

hal.structure.identifierINSTITUT FUER ANALYSIS
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHAAK, Bernhard H.
hal.structure.identifierINSTITUT FUER ANALYSIS
dc.contributor.authorKUNSTMANN, Peer Christian
dc.date.accessioned2024-04-04T02:53:03Z
dc.date.available2024-04-04T02:53:03Z
dc.date.issued2007
dc.identifier.issn0363-0129
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192134
dc.description.abstractEnWe study linear control systems in infinite-dimensional Banach spaces governed by analytic semigroups. For $p\in[1,\infty]$ and $\alpha\in\mathbb{R}$ we introduce the notion of $L^p$-admissibility of type $\alpha$ for unbounded observation and control operators. Generalizing earlier work by Le~Merdy [{\it J. London Math. Soc.} (2), 67 (2003), pp.~715--738] and Haak and Le~Merdy [{\it Houston J. Math.}, 31 (2005), pp.~1153--1167], we give conditions under which $L^p$-admissibility of type $\alpha$ is characterized by boundedness conditions which are similar to those in the well-known Weiss conjecture. We also study $L^p$-wellposedness of type $\alpha$ for the full system. Here we use recent ideas due to Pruess and Simonett [{\it Arch. Math. (Basel)}, 82 (2004), pp. 415--431]. Our results are illustrated by a controlled heat equation with boundary control and boundary observation where we take Lebesgue and Besov spaces as state space. This extends the considerations in [C. I. Byrnes et al., {\it J. Dynam. Control Systems}, 8 (2002), pp.~341--370] to non-Hilbertian settings and to $p\neq 2$.
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.encontrol theory
dc.subject.enlinear systems
dc.subject.enadmissibility
dc.subject.en$H^\infty$-calculus
dc.subject.ensquare-function estimates
dc.title.enWeighted Admissibility and Wellposedness of Linear Systems in Banach Spaces
dc.typeArticle de revue
bordeaux.journalSIAM Journal on Control and Optimization
bordeaux.page2094-2118
bordeaux.volume45
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue6
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00281622
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00281622v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Control%20and%20Optimization&rft.date=2007&rft.volume=45&rft.issue=6&rft.spage=2094-2118&rft.epage=2094-2118&rft.eissn=0363-0129&rft.issn=0363-0129&rft.au=HAAK,%20Bernhard%20H.&KUNSTMANN,%20Peer%20Christian&rft.genre=article


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