Further Qualitative Results for Second-Order Dynamical Systems Based on Circuit Theory Approach

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dc.authoridMINAZ, Mehmet Recep/0000-0001-8046-6465
dc.contributor.authorAtes, Muhammet
dc.contributor.authorMinaz, Mehmet Recep
dc.date.accessioned2024-12-24T19:24:23Z
dc.date.available2024-12-24T19:24:23Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractIn this study, our goal is to construct mathematical models of some physical systems and then determine their qualitative behaviors by Lyapunov's direct method. The constructed systems are governed by second-order vector ordinary differential equations. Our main system involves three nonlinear elements that generalize the previously studied systems. For each system, we construct the associated energy or storage or Lyapunov function from the physical implication of the system which is based on basic circuit theory. We use the power-energy relationship to construct the Lyapunov function for each system. The directional derivative of each function gives the negative value of the dissipative power in the system. These two technics may not be clear in the literature. Thus, the proposed approach simplifies the derivative of Lyapunov functions which are written in integration and improves some well-known results. For a physical system, we insist that the Lyapunov function and its directional derivate are unique. Our discussion includes four new results associated with the stability theory of dynamical systems. We also give a new passivity result for our main system. Finally, we give an example with simulations to elucidate the theoretical results.
dc.identifier.doi10.1007/s00034-022-02027-1
dc.identifier.endpage4774
dc.identifier.issn0278-081X
dc.identifier.issn1531-5878
dc.identifier.issue9
dc.identifier.scopus2-s2.0-85128954597
dc.identifier.scopusqualityQ1
dc.identifier.startpage4755
dc.identifier.urihttps://doi.org/10.1007/s00034-022-02027-1
dc.identifier.urihttps://hdl.handle.net/20.500.12604/5965
dc.identifier.volume41
dc.identifier.wosWOS:000788482600001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Birkhauser
dc.relation.ispartofCircuits Systems and Signal Processing
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectLRC circuits
dc.subjectLyapunov stability
dc.subjectSecond-order differential equations
dc.subjectPassivity
dc.titleFurther Qualitative Results for Second-Order Dynamical Systems Based on Circuit Theory Approach
dc.typeArticle

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