Lyapunov - Кrasovskii functionals for homogeneous systems with multiple delays

Standard

Lyapunov - Кrasovskii functionals for homogeneous systems with multiple delays. / Alexandrova, I. V.; Zhabko, A. P.

In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Vol. 17, No. 2, 2021, p. 183-195.

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

Author

Alexandrova, I. V. ; Zhabko, A. P. / Lyapunov - Кrasovskii functionals for homogeneous systems with multiple delays. In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2021 ; Vol. 17, No. 2. pp. 183-195.

BibTeX

@article{74c63759b1f14606bdb16544d026980f,

title = "Lyapunov - Кrasovskii functionals for homogeneous systems with multiple delays",

abstract = "In this article, explicit constructions of Lyapunov - Krasovskii functionals are proposed for homogeneous systems with multiple constant delays and homogeneity degree of the right-hand sides strictly greater than one. The constructions are based on the Lyapunov functions suitable for the analysis of corresponding systems with all delays equal to zero. The letter systems are assumed to be asymptotically stable. It is proved that the proposed functionals satisfy the conditions of the Krasovskii theorem, and hence it allows us to establish the asymptotic stability of the trivial solution for arbitrary values of delays. The functionals are applied to the estimation of the attraction region of the trivial solution.",

keywords = "Asymptotic stability, Attraction region, Homogeneous systems, Lyapunov - Krasovskii functionals, Time delay systems, time delay systems, homogeneous systems, attraction region, asymptotic stability, Lyapunov-Krasovskii functionals",

author = "Alexandrova, {I. V.} and Zhabko, {A. P.}",

year = "2021",

doi = "10.21638/11701/SPBU10.2021.208",

language = "English",

volume = "17",

pages = "183--195",

journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1811-9905",

publisher = "Издательство Санкт-Петербургского университета",

number = "2",

}

RIS

TY - JOUR

T1 - Lyapunov - Кrasovskii functionals for homogeneous systems with multiple delays

AU - Alexandrova, I. V.

AU - Zhabko, A. P.

PY - 2021

Y1 - 2021

N2 - In this article, explicit constructions of Lyapunov - Krasovskii functionals are proposed for homogeneous systems with multiple constant delays and homogeneity degree of the right-hand sides strictly greater than one. The constructions are based on the Lyapunov functions suitable for the analysis of corresponding systems with all delays equal to zero. The letter systems are assumed to be asymptotically stable. It is proved that the proposed functionals satisfy the conditions of the Krasovskii theorem, and hence it allows us to establish the asymptotic stability of the trivial solution for arbitrary values of delays. The functionals are applied to the estimation of the attraction region of the trivial solution.

AB - In this article, explicit constructions of Lyapunov - Krasovskii functionals are proposed for homogeneous systems with multiple constant delays and homogeneity degree of the right-hand sides strictly greater than one. The constructions are based on the Lyapunov functions suitable for the analysis of corresponding systems with all delays equal to zero. The letter systems are assumed to be asymptotically stable. It is proved that the proposed functionals satisfy the conditions of the Krasovskii theorem, and hence it allows us to establish the asymptotic stability of the trivial solution for arbitrary values of delays. The functionals are applied to the estimation of the attraction region of the trivial solution.

KW - Asymptotic stability

KW - Attraction region

KW - Homogeneous systems

KW - Lyapunov - Krasovskii functionals

KW - Time delay systems

KW - time delay systems

KW - homogeneous systems

KW - attraction region

KW - asymptotic stability

KW - Lyapunov-Krasovskii functionals

UR - http://www.scopus.com/inward/record.url?scp=85112014756&partnerID=8YFLogxK

U2 - 10.21638/11701/SPBU10.2021.208

DO - 10.21638/11701/SPBU10.2021.208

M3 - Article

AN - SCOPUS:85112014756

VL - 17

SP - 183

EP - 195

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 2

ER -

ID: 85683384