An explicit Floquet-type representation of Riccati aperiodic exponential semigroups

Bishop, AN; Del Moral, P

An explicit Floquet-type representation of Riccati aperiodic exponential semigroups

Bishop, AN

Del Moral, P

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Publication Type:: Journal Article
Citation:: International Journal of Control, 2019
Issue Date:: 2019-01-01

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Field	Value	Language
dc.contributor.author	Bishop, AN https://orcid.org/0000-0001-8581-8562	en_US
dc.contributor.author	Del Moral, P	en_US
dc.date.issued	2019-01-01	en_US
dc.identifier.citation	International Journal of Control, 2019	en_US
dc.identifier.issn	0020-7179	en_US
dc.identifier.uri	http://hdl.handle.net/10453/133035
dc.description.abstract	© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group. The article presents a rather surprising Floquet-type representation of time-varying transition matrices associated with a class of nonlinear matrix differential Riccati equations. The main difference with conventional Floquet theory comes from the fact that the underlying flow of the solution matrix is aperiodic. The monodromy matrix associated with this Floquet representation coincides with the exponential (fundamental) matrix associated with the stabilising fixed point of the Riccati equation. The second part of this article is dedicated to the application of this representation to the stability of matrix differential Riccati equations. We provide refined global and local contraction inequalities for the Riccati exponential semigroup that depend linearly on the spectral norm of the initial condition. These refinements improve upon existing results and are a direct consequence of the Floquet-type representation, yielding what seems to be the first results of this type for this class of models.	en_US
dc.relation.ispartof	International Journal of Control	en_US
dc.relation.isbasedon	10.1080/00207179.2019.1590647	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject.classification	Industrial Engineering & Automation	en_US
dc.title	An explicit Floquet-type representation of Riccati aperiodic exponential semigroups	en_US
dc.type	Journal Article
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	0913 Mechanical Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
utslib.copyright.status	closed_access	*
pubs.publication-status	Published	en_US

Abstract:

© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group. The article presents a rather surprising Floquet-type representation of time-varying transition matrices associated with a class of nonlinear matrix differential Riccati equations. The main difference with conventional Floquet theory comes from the fact that the underlying flow of the solution matrix is aperiodic. The monodromy matrix associated with this Floquet representation coincides with the exponential (fundamental) matrix associated with the stabilising fixed point of the Riccati equation. The second part of this article is dedicated to the application of this representation to the stability of matrix differential Riccati equations. We provide refined global and local contraction inequalities for the Riccati exponential semigroup that depend linearly on the spectral norm of the initial condition. These refinements improve upon existing results and are a direct consequence of the Floquet-type representation, yielding what seems to be the first results of this type for this class of models.

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http://hdl.handle.net/10453/133035