Limit Properties of a Sequence of Lyapunov’s Integrals Determined by a System of High-Dimensional Differential Equations

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Limit Properties of a Sequence of Lyapunov’s Integrals Determined by a System of High-Dimensional Differential Equations. / Il’inykh, I. D.

In: Siberian Advances in Mathematics, Vol. 36, No. 1, 15.06.2026, p. 22-42.

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

BibTeX

@article{b3d6d87f70ad495e97d06b2454ea3598,

title = "Limit Properties of a Sequence of Lyapunov{\textquoteright}s Integrals Determined by a System of High-Dimensional Differential Equations",

abstract = "We consider a delay differential equation together with a sequence of high-dimensionalsystems of ordinary differential equations. We establish a connection between the regions ofasymptotic stability of their zero solutions and study limit properties of the sequence ofLyapunov{\textquoteright}s integrals.",

keywords = "Lyapunov equation, delay differential equation, high-dimensional system of ordinary differential equations, stability, дифференциальное уравнение с запаздыванием, многомерная система обыкновенных дифференциальных уравнений, устойчивость, уравнение Ляпунова",

author = "Il{\textquoteright}inykh, {I. D.}",

note = "Il'inykh, I. D. Limit Properties of a Sequence of Lyapunov's Integrals Determined by a System of High-Dimensional Differential Equations / I. D. Il'inykh // Siberian Advances in Mathematics. – 2026. – Vol. 36, No. 1. – P. 22-42. – DOI 10.1134/S1055134426010037. – EDN XJHEHA. The work was partially supported by the Mathematical Center in Akademgorodok (agreement 075-15-2025-349 with the Ministry of Science and Higher Education of the Russian Federation).",

year = "2026",

month = jun,

day = "15",

doi = "10.1134/S1055134426010037",

language = "English",

volume = "36",

pages = "22--42",

journal = "Siberian Advances in Mathematics",

issn = "1055-1344",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Limit Properties of a Sequence of Lyapunov’s Integrals Determined by a System of High-Dimensional Differential Equations

AU - Il’inykh, I. D.

N1 - Il'inykh, I. D. Limit Properties of a Sequence of Lyapunov's Integrals Determined by a System of High-Dimensional Differential Equations / I. D. Il'inykh // Siberian Advances in Mathematics. – 2026. – Vol. 36, No. 1. – P. 22-42. – DOI 10.1134/S1055134426010037. – EDN XJHEHA. The work was partially supported by the Mathematical Center in Akademgorodok (agreement 075-15-2025-349 with the Ministry of Science and Higher Education of the Russian Federation).

PY - 2026/6/15

Y1 - 2026/6/15

N2 - We consider a delay differential equation together with a sequence of high-dimensionalsystems of ordinary differential equations. We establish a connection between the regions ofasymptotic stability of their zero solutions and study limit properties of the sequence ofLyapunov’s integrals.

AB - We consider a delay differential equation together with a sequence of high-dimensionalsystems of ordinary differential equations. We establish a connection between the regions ofasymptotic stability of their zero solutions and study limit properties of the sequence ofLyapunov’s integrals.

KW - Lyapunov equation

KW - delay differential equation

KW - high-dimensional system of ordinary differential equations

KW - stability

KW - дифференциальное уравнение с запаздыванием

KW - многомерная система обыкновенных дифференциальных уравнений

KW - устойчивость

KW - уравнение Ляпунова

UR - https://www.mendeley.com/catalogue/250a8cd5-86a5-38f7-a688-fecfb73382ae/

UR - https://www.scopus.com/pages/publications/105041813484

UR - https://elibrary.ru/item.asp?id=91603124

U2 - 10.1134/S1055134426010037

DO - 10.1134/S1055134426010037

M3 - Article

VL - 36

SP - 22

EP - 42

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -

ID: 85086615