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On the Asymptotic Stability of Nonlinear Mechanical Switched Systems. / Платонов, Алексей Викторович.

в: AIP Conference Proceedings, Том 1959, 080019, 02.05.2018.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Платонов, АВ 2018, 'On the Asymptotic Stability of Nonlinear Mechanical Switched Systems', AIP Conference Proceedings, Том. 1959, 080019. https://doi.org/10.1063/1.5034736

APA

Платонов, А. В. (2018). On the Asymptotic Stability of Nonlinear Mechanical Switched Systems. AIP Conference Proceedings, 1959, [080019]. https://doi.org/10.1063/1.5034736

Vancouver

Платонов АВ. On the Asymptotic Stability of Nonlinear Mechanical Switched Systems. AIP Conference Proceedings. 2018 Май 2;1959. 080019. https://doi.org/10.1063/1.5034736

Author

Платонов, Алексей Викторович. / On the Asymptotic Stability of Nonlinear Mechanical Switched Systems. в: AIP Conference Proceedings. 2018 ; Том 1959.

BibTeX

@article{2991ce899df2418e8caf118ae4584edc,
title = "On the Asymptotic Stability of Nonlinear Mechanical Switched Systems",
abstract = "Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.",
author = "Платонов, {Алексей Викторович}",
note = "Funding Information: This work was supported by the Russian Foundation of Basic Researches, grant no. 16-01-00587.",
year = "2018",
month = may,
day = "2",
doi = "10.1063/1.5034736",
language = "English",
volume = "1959",
journal = "AIP Conference Proceedings",
issn = "0094-243X",
publisher = "American Institute of Physics",

}

RIS

TY - JOUR

T1 - On the Asymptotic Stability of Nonlinear Mechanical Switched Systems

AU - Платонов, Алексей Викторович

N1 - Funding Information: This work was supported by the Russian Foundation of Basic Researches, grant no. 16-01-00587.

PY - 2018/5/2

Y1 - 2018/5/2

N2 - Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

AB - Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

UR - http://www.scopus.com/inward/record.url?scp=85047178528&partnerID=8YFLogxK

U2 - 10.1063/1.5034736

DO - 10.1063/1.5034736

M3 - Article

VL - 1959

JO - AIP Conference Proceedings

JF - AIP Conference Proceedings

SN - 0094-243X

M1 - 080019

ER -

ID: 26593331