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hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorHORTON, Emma
dc.date.accessioned2024-04-04T02:46:05Z
dc.date.available2024-04-04T02:46:05Z
dc.date.issued2022
dc.identifier.issn0363-0129
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191517
dc.description.abstractEnDiscrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article we provide a self-contained study of discrete time Riccati matrix difference equations. In particular, we provide a novel Riccati semigroup duality formula and a new Floquet-type representation for these equations. Due to the aperiodicity of the underlying flow of the solution matrix, conventional Floquet theory does not apply in this setting and thus further analysis is required. We illustrate the impact of these formulae with an explicit description of the solution of time-varying Riccati difference equations and its fundamental-type solution in terms of the fixed point of the equation and an invertible linear matrix map, as well as uniform upper and lower bounds on the Riccati maps. These are the first results of this type for time varying Riccati matrix difference equations.
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.enRiccati matrix difference equations
dc.subject.enDiscrete time algebraic Riccati equation
dc.subject.enSherman-Morrison-Woodbury inversion identity
dc.subject.enGramian matrix
dc.subject.enMatrix positive definite maps
dc.subject.enFloquet theory
dc.subject.enSemigroup duality formula
dc.subject.enLyapunov equations
dc.title.enA note on Riccati matrix difference equations
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv2107.12918
bordeaux.journalSIAM Journal on Control and Optimization
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03299378
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03299378v1
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=2022&rft.eissn=0363-0129&rft.issn=0363-0129&rft.au=DEL%20MORAL,%20Pierre&HORTON,%20Emma&rft.genre=article


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