On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition

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dc.contributor.authorLhachemi, Hugo-
dc.contributor.authorShorten, Robert-
dc.date.accessioned2022-01-14T16:23:18Z-
dc.date.available2022-01-14T16:23:18Z-
dc.date.copyright2020 IEEEen_US
dc.date.issued2021-11-
dc.identifier.citationIEEE Transactions on Automatic Controlen_US
dc.identifier.urihttp://hdl.handle.net/10197/12733-
dc.description.abstractStability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov-Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efficient tools for the study of the stability properties. However, in such an approach the initial condition needs to be assumed absolutely continuous with a square integrable weak derivative. In addition, the stability results hold for initial conditions that are evaluated based on the magnitude of both the initial condition and its time-derivative. The main objective of this paper is to show that, for certain classes of time-delay systems, the aforementioned stability results can actually be extended to initial conditions that are only assumed continuous and that are evaluated in uniform norm.en_US
dc.description.sponsorshipEuropean Commission - European Regional Development Funden_US
dc.description.sponsorshipScience Foundation Irelanden_US
dc.language.isoenen_US
dc.publisherIEEEen_US
dc.rights© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.en_US
dc.subjectTime-delay systemsen_US
dc.subjectRetarded differential equationsen_US
dc.subjectLyapunov-Krasovskii functionalsen_US
dc.subjectStability propertiesen_US
dc.subjectRegularity of the initial conditionen_US
dc.titleOn the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial conditionen_US
dc.typeJournal Articleen_US
dc.statusPeer revieweden_US
dc.identifier.volume66en_US
dc.identifier.issue11en_US
dc.identifier.startpage5401en_US
dc.identifier.endpage5406en_US
dc.identifier.doi10.1109/TAC.2020.3047358-
dc.neeo.contributorLhachemi|Hugo|aut|-
dc.neeo.contributorShorten|Robert|aut|-
dc.identifier.grantid16/RC/3872-
dc.rights.licensehttps://creativecommons.org/licenses/by-nc-nd/3.0/ie/en_US
item.fulltextWith Fulltext-
item.grantfulltextopen-
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