Standard

Stability analysis for a class of mechanical systems with piecewise constant coefficients. / Platonov, Alexey .

In: Journal of Physics: Conference Series, Vol. 1959, No. 1, 012037, 14.07.2021.

Research output: Contribution to journal › Conference article › peer-review

Harvard

Platonov, A 2021, 'Stability analysis for a class of mechanical systems with piecewise constant coefficients', Journal of Physics: Conference Series, vol. 1959, no. 1, 012037. https://doi.org/10.1088/1742-6596/1959/1/012037

APA

Platonov, A. (2021). Stability analysis for a class of mechanical systems with piecewise constant coefficients. Journal of Physics: Conference Series, 1959(1), [012037]. https://doi.org/10.1088/1742-6596/1959/1/012037

Vancouver

Platonov A. Stability analysis for a class of mechanical systems with piecewise constant coefficients. Journal of Physics: Conference Series. 2021 Jul 14;1959(1). 012037. https://doi.org/10.1088/1742-6596/1959/1/012037

Author

Platonov, Alexey . / Stability analysis for a class of mechanical systems with piecewise constant coefficients. In: Journal of Physics: Conference Series. 2021 ; Vol. 1959, No. 1.

BibTeX

@article{c373bc2b636749a680a080070d2119f5,
title = "Stability analysis for a class of mechanical systems with piecewise constant coefficients",
abstract = "A nonlinear mechanical system described by a vector equation of the Lienard type is considered. It is assumed that the forces acting on the mechanical system are given by functions that are piecewise constant with respect to time. With the aid of a special variable substitution, the equation is reduced to a system that can be considered as an impulsive switched system with infinite numbers of operating modes. The stability problem for the trivial equilibrium position of the obtained system is studied. The stability analysis is carried out using a specially constructed discontinuous Lyapunov function. This function can be understood as a multiple Lyapunov function, consisting of an infinite number of partial Lyapunov functions, each of which is used for a certain time interval. Differentiating the chosen Lyapunov function with respect to solutions of the given system on the corresponding time intervals and applying the theory of differential inequalities, sufficient conditions of the asymptotic stability of the equilibrium position are established.",
author = "Alexey Platonov",
note = "Alexey Platonov 2021 J. Phys.: Conf. Ser. 1959 012037; null ; Conference date: 09-03-2021 Through 12-03-2021",
year = "2021",
month = jul,
day = "14",
doi = "10.1088/1742-6596/1959/1/012037",
language = "English",
volume = "1959",
journal = "Journal of Physics: Conference Series",
issn = "1742-6588",
publisher = "IOP Publishing Ltd.",
number = "1",

}

RIS

TY - JOUR

T1 - Stability analysis for a class of mechanical systems with piecewise constant coefficients

AU - Platonov, Alexey

N1 - Alexey Platonov 2021 J. Phys.: Conf. Ser. 1959 012037

PY - 2021/7/14

Y1 - 2021/7/14

N2 - A nonlinear mechanical system described by a vector equation of the Lienard type is considered. It is assumed that the forces acting on the mechanical system are given by functions that are piecewise constant with respect to time. With the aid of a special variable substitution, the equation is reduced to a system that can be considered as an impulsive switched system with infinite numbers of operating modes. The stability problem for the trivial equilibrium position of the obtained system is studied. The stability analysis is carried out using a specially constructed discontinuous Lyapunov function. This function can be understood as a multiple Lyapunov function, consisting of an infinite number of partial Lyapunov functions, each of which is used for a certain time interval. Differentiating the chosen Lyapunov function with respect to solutions of the given system on the corresponding time intervals and applying the theory of differential inequalities, sufficient conditions of the asymptotic stability of the equilibrium position are established.

AB - A nonlinear mechanical system described by a vector equation of the Lienard type is considered. It is assumed that the forces acting on the mechanical system are given by functions that are piecewise constant with respect to time. With the aid of a special variable substitution, the equation is reduced to a system that can be considered as an impulsive switched system with infinite numbers of operating modes. The stability problem for the trivial equilibrium position of the obtained system is studied. The stability analysis is carried out using a specially constructed discontinuous Lyapunov function. This function can be understood as a multiple Lyapunov function, consisting of an infinite number of partial Lyapunov functions, each of which is used for a certain time interval. Differentiating the chosen Lyapunov function with respect to solutions of the given system on the corresponding time intervals and applying the theory of differential inequalities, sufficient conditions of the asymptotic stability of the equilibrium position are established.

UR - https://iopscience.iop.org/article/10.1088/1742-6596/1959/1/012037/pdf

UR - https://iopscience.iop.org/article/10.1088/1742-6596/1959/1/012037

UR - http://www.scopus.com/inward/record.url?scp=85111984505&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1959/1/012037

DO - 10.1088/1742-6596/1959/1/012037

M3 - Conference article

VL - 1959

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012037

Y2 - 9 March 2021 through 12 March 2021

ER -

ID: 78885103