Almost global stability of nonlinear switched systems with time-dependent switching

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dc.authorscopusid24824407000
dc.authorscopusid57144457100
dc.authorscopusid23394098500
dc.contributor.authorKarabacak, Özkan
dc.contributor.authorKıvılcım, Ayşegül
dc.contributor.authorWisniewski, Rafael
dc.date.accessioned2022-02-15T16:57:56Z
dc.date.available2022-02-15T16:57:56Z
dc.date.issued2020
dc.departmentBakırçay Üniversitesien_US
dc.description.abstractFor a dynamical system, it is known that the existence of a Lyapunov density implies almost global stability of an equilibrium. It is then natural to ask whether the existence of multiple Lyapunov densities for a nonlinear switched system implies almost global stability, in the same way as the existence of multiple Lyapunov functions implies global stability for nonlinear switched systems. In this paper, the answer to this question is shown to be affirmative as long as switchings satisfy a dwell time constraint with an arbitrarily small dwell time. Specifically, as the main result, we show that a nonlinear switched system with a minimum dwell time is almost globally stable if there exist multiple Lyapunov densities that satisfy some compatibility conditions depending on the value of the minimum dwell time. This result can also be used to obtain a minimum dwell time estimate to ensure almost global stability of a nonlinear switched systems. In particular, the existence of a common Lyapunov density implies almost global stability for any arbitrary small minimum dwell time. The results obtained for continuous-time switched systems are based on some sufficient conditions for the almost global stability of discrete-time nonautonomous systems. These conditions are obtained using the duality between Frobenius-Perron operator and Koopman operator. © 1963-2012 IEEE.en_US
dc.description.sponsorshipDanmarks Frie Forskningsfond, DFFen_US
dc.description.sponsorshipManuscript received February 14, 2019; accepted June 30, 2019. Date of publication July 10, 2019; date of current version June 27, 2020. This work was supported by the Independent Research Fund Denmark under Project DeBaTe and Project CodeMe. Recommended by Associate Editor S. Tarbouriech. (Corresponding author: Özkan Karabacak.) Ö. Karabacak is with the Department of Electronic Systems, Automation and Control, Aalborg University, 9220 Aalborg, Denmark. He is also with the University of Bakırc¸cay, Department of Electrical and Electronics Engineering, 35665 Menemen/Seyrek, İzmir, Turkey (e-mail:, ozk@es.aau.dk).en_US
dc.identifier.doi10.1109/TAC.2019.2927934
dc.identifier.endpage2978en_US
dc.identifier.issn0018-9286
dc.identifier.issue7en_US
dc.identifier.scopus2-s2.0-85087791463en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage2969en_US
dc.identifier.urihttps://doi.org/10.1109/TAC.2019.2927934
dc.identifier.urihttps://hdl.handle.net/20.500.14034/311
dc.identifier.volume65en_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherInstitute of Electrical and Electronics Engineers Inc.en_US
dc.relation.journalIEEE Transactions on Automatic Controlen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectAlmost global stabilityen_US
dc.subjectcommon Lyapunov densityen_US
dc.subjectminimum dwell timeen_US
dc.subjectmultiple Lyapunov densitiesen_US
dc.subjectnonlinear switched systemsen_US
dc.subjectDynamical systemsen_US
dc.subjectLyapunov functionsen_US
dc.subjectSystem stabilityen_US
dc.subjectAlmost global stabilityen_US
dc.subjectCompatibility conditionsen_US
dc.subjectFrobenius-Perron operatorsen_US
dc.subjectGlobal stabilityen_US
dc.subjectMinimum dwell timeen_US
dc.subjectMultiple Lyapunov functionen_US
dc.subjectNon-autonomous systemen_US
dc.subjectNonlinear switched systemsen_US
dc.subjectContinuous time systemsen_US
dc.titleAlmost global stability of nonlinear switched systems with time-dependent switchingen_US
dc.typeArticleen_US

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