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dc.contributor.authorKuznetsov, N. V.
dc.contributor.authorKuznetsova, O. A.
dc.contributor.authorMokaev, T. N.
dc.contributor.authorMokaev, R. N.
dc.contributor.authorYuldashev, M. V.
dc.contributor.authorYuldashev, R. V.
dc.contributor.editorJadachowski, Lukaz
dc.date.accessioned2021-08-03T11:38:20Z
dc.date.available2021-08-03T11:38:20Z
dc.date.issued2019
dc.identifier.citationKuznetsov, N. V., Kuznetsova, O. A., Mokaev, T. N., Mokaev, R. N., Yuldashev, M. V., & Yuldashev, R. V. (2019). Coexistence of hidden attractors and multistability in counterexamples to the Kalman conjecture. In L. Jadachowski (Ed.), <i>11th IFAC Symposium on Nonlinear Control Systems NOLCOS 2019 Vienna, Austria, 4-6 September 2019</i> (52, pp. 7-12). IFAC; Elsevier. IFAC-PapersOnLine. <a href="https://doi.org/10.1016/j.ifacol.2019.11.747" target="_blank">https://doi.org/10.1016/j.ifacol.2019.11.747</a>
dc.identifier.otherCONVID_33903502
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/77272
dc.description.abstractThe Aizerman and Kalman conjectures played an important role in the theory of global stability for control systems and set two directions for its further development – the search and formulation of sufficient stability conditions, as well as the construction of counterexamples for these conjectures. From the computational perspective the latter problem is nontrivial, since the oscillations in counterexamples are hidden, i.e. their basin of attraction does not intersect with a small neighborhood of an equilibrium. Numerical calculation of initial data of such oscillations for their visualization is a challenging problem. Up to now all known counterexamples to the Kalman conjecture were constructed in such a way that one locally stable limit cycle (hidden oscillation) co-exists with a locally stable equilibrium. In this paper we demonstrate a multistable configuration of three co-existing hidden oscillations (limit cycles) and a locally stable equilibrium in the phase space of the fourth-order system, which provides a new class of counterexamples to the Kalman conjecture.en
dc.format.extent842
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherIFAC; Elsevier
dc.relation.ispartof11th IFAC Symposium on Nonlinear Control Systems NOLCOS 2019 Vienna, Austria, 4-6 September 2019
dc.relation.ispartofseriesIFAC-PapersOnLine
dc.rightsCC BY-NC-ND 4.0
dc.subject.otherglobal stability
dc.subject.otherhidden attractors
dc.subject.othermultistability
dc.subject.otherKalman conjecture
dc.subject.otherperiodic oscillations
dc.titleCoexistence of hidden attractors and multistability in counterexamples to the Kalman conjecture
dc.typeconferenceObject
dc.identifier.urnURN:NBN:fi:jyu-202108034440
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.type.urihttp://purl.org/eprint/type/ConferencePaper
dc.description.reviewstatuspeerReviewed
dc.format.pagerange7-12
dc.relation.issn2405-8971
dc.relation.numberinseries16
dc.relation.volume52
dc.type.versionpublishedVersion
dc.rights.copyright© 2019 IFAC
dc.rights.accesslevelopenAccessfi
dc.relation.conferenceIFAC Symposium on Nonlinear Control Systems
dc.subject.ysovärähtelyt
dc.subject.ysosäätöteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p708
jyx.subject.urihttp://www.yso.fi/onto/yso/p868
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1016/j.ifacol.2019.11.747
jyx.fundinginformationWe acknowledge support form the Russian Scientific Foundation (project 19-41-02002, sections 2-4) and the Leading Scientific Schools of Russia (project NSh-2858.2018.1, section 1).


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