Standard

Исследование асимптотической устойчивости нулевого решения для одного класса нелинейных нестационарных систем методом усреднения. / Александров, Александр Юрьевич.

In: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, No. 2, 2023, p. 28-41.

Research output: Contribution to journal › Article › peer-review

Harvard

Александров, АЮ 2023, 'Исследование асимптотической устойчивости нулевого решения для одного класса нелинейных нестационарных систем методом усреднения', ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, no. 2, pp. 28-41. https://doi.org/10.21638/11701/spbu35.2023.202

APA

Александров, А. Ю. (2023). Исследование асимптотической устойчивости нулевого решения для одного класса нелинейных нестационарных систем методом усреднения. ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, (2), 28-41. https://doi.org/10.21638/11701/spbu35.2023.202

Vancouver

Александров АЮ. Исследование асимптотической устойчивости нулевого решения для одного класса нелинейных нестационарных систем методом усреднения. ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ. 2023;(2):28-41. https://doi.org/10.21638/11701/spbu35.2023.202

Author

Александров, Александр Юрьевич. / Исследование асимптотической устойчивости нулевого решения для одного класса нелинейных нестационарных систем методом усреднения. In: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ. 2023 ; No. 2. pp. 28-41.

BibTeX

@article{050dc49f01034c6793e280c7a69323db,
title = "Исследование асимптотической устойчивости нулевого решения для одного класса нелинейных нестационарных систем методом усреднения",
abstract = "A system of nonlinear differential equations is considered that describes the interaction of two coupled subsystems, one of these subsystems is linear, and the other is nonlinear and homogeneous with an order of homogeneity greater than one. It is assumed that this system is affected by nonstationary perturbations with zero mean values. Using the averaging method, su cient conditions are determined under which perturbations do not disturb the asymptotic stability of the zero solution. The derivation of these conditions is based on the use of a special construction of the nonstationary Lyapunov function which takes into account the structure of the acting perturbations. In addition, we consider the case where there is a constant delay in the right-hand sides of the system. An original approach to the construction of the Lyapunov-Krasovskii functional for such a system is proposed. Using this functional, conditions are found that guarantee the preservation of the asymptotic stability for any positive delay.",
keywords = "asymptotic stability, averaging, delay, nonlinear systems, nonstationary perturbations, the Lyapunov direct method",
author = "Александров, {Александр Юрьевич}",
year = "2023",
doi = "10.21638/11701/spbu35.2023.202",
language = "русский",
pages = "28--41",
journal = "ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ",
issn = "1817-2172",
publisher = "Электронный журнал {"}Дифференциальные уравнения и процессы управления{"}",
number = "2",

}

RIS

TY - JOUR

T1 - Исследование асимптотической устойчивости нулевого решения для одного класса нелинейных нестационарных систем методом усреднения

AU - Александров, Александр Юрьевич

PY - 2023

Y1 - 2023

N2 - A system of nonlinear differential equations is considered that describes the interaction of two coupled subsystems, one of these subsystems is linear, and the other is nonlinear and homogeneous with an order of homogeneity greater than one. It is assumed that this system is affected by nonstationary perturbations with zero mean values. Using the averaging method, su cient conditions are determined under which perturbations do not disturb the asymptotic stability of the zero solution. The derivation of these conditions is based on the use of a special construction of the nonstationary Lyapunov function which takes into account the structure of the acting perturbations. In addition, we consider the case where there is a constant delay in the right-hand sides of the system. An original approach to the construction of the Lyapunov-Krasovskii functional for such a system is proposed. Using this functional, conditions are found that guarantee the preservation of the asymptotic stability for any positive delay.

AB - A system of nonlinear differential equations is considered that describes the interaction of two coupled subsystems, one of these subsystems is linear, and the other is nonlinear and homogeneous with an order of homogeneity greater than one. It is assumed that this system is affected by nonstationary perturbations with zero mean values. Using the averaging method, su cient conditions are determined under which perturbations do not disturb the asymptotic stability of the zero solution. The derivation of these conditions is based on the use of a special construction of the nonstationary Lyapunov function which takes into account the structure of the acting perturbations. In addition, we consider the case where there is a constant delay in the right-hand sides of the system. An original approach to the construction of the Lyapunov-Krasovskii functional for such a system is proposed. Using this functional, conditions are found that guarantee the preservation of the asymptotic stability for any positive delay.

KW - asymptotic stability

KW - averaging

KW - delay

KW - nonlinear systems

KW - nonstationary perturbations

KW - the Lyapunov direct method

UR - https://diffjournal.spbu.ru/RU/numbers/2023.2/article.1.2.html

UR - https://www.mendeley.com/catalogue/1a799809-fa86-3073-9740-7fcb2b35e9f3/

U2 - 10.21638/11701/spbu35.2023.202

DO - 10.21638/11701/spbu35.2023.202

M3 - статья

SP - 28

EP - 41

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 2

ER -

ID: 107088425