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The Second Lyapunov Method for Time-Delay Systems. / Demidenko, G. V.; Matveeva, I. I.

Functional Differential Equations and Applications - FDEA-2019. ed. / Alexander Domoshnitsky; Alexander Rasin; Seshadev Padhi. 1. ed. Springer, Cham, 2021. p. 145-167 (Springer Proceedings in Mathematics and Statistics; Vol. 379).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Demidenko, GV & Matveeva, II 2021, The Second Lyapunov Method for Time-Delay Systems. in A Domoshnitsky, A Rasin & S Padhi (eds), Functional Differential Equations and Applications - FDEA-2019. 1 edn, Springer Proceedings in Mathematics and Statistics, vol. 379, Springer, Cham, pp. 145-167, 7th International Conference on Functional Differential Equations and Applications, FDEA 2019, Ariel, Israel, 22.08.2019. https://doi.org/10.1007/978-981-16-6297-3_11

APA

Demidenko, G. V., & Matveeva, I. I. (2021). The Second Lyapunov Method for Time-Delay Systems. In A. Domoshnitsky, A. Rasin, & S. Padhi (Eds.), Functional Differential Equations and Applications - FDEA-2019 (1 ed., pp. 145-167). (Springer Proceedings in Mathematics and Statistics; Vol. 379). Springer, Cham. https://doi.org/10.1007/978-981-16-6297-3_11

Vancouver

Demidenko GV, Matveeva II. The Second Lyapunov Method for Time-Delay Systems. In Domoshnitsky A, Rasin A, Padhi S, editors, Functional Differential Equations and Applications - FDEA-2019. 1 ed. Springer, Cham. 2021. p. 145-167. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-981-16-6297-3_11

Author

Demidenko, G. V. ; Matveeva, I. I. / The Second Lyapunov Method for Time-Delay Systems. Functional Differential Equations and Applications - FDEA-2019. editor / Alexander Domoshnitsky ; Alexander Rasin ; Seshadev Padhi. 1. ed. Springer, Cham, 2021. pp. 145-167 (Springer Proceedings in Mathematics and Statistics).

BibTeX

@inproceedings{82ea3efc058e40f1906986c93b6f5e7b,
title = "The Second Lyapunov Method for Time-Delay Systems",
abstract = "Some classes of systems of delay differential equations are considered. We give a review of methods for the study of the stability of solutions in the case of constant and periodic coefficients in linear terms. Special attention is paid to the development of the second Lyapunov method. A number of authors{\textquoteright} results for linear and nonlinear delay differential equations obtained by using various Lyapunov–Krasovskii functionals are presented. The application of discrete analogs of the constructed functionals to the study of the stability of solutions to delay difference equations is discussed.",
keywords = "Estimates for solutions, Exponential stability, Lyapunov-Krasovskii functionals, Periodic coefficients, Time-delay systems",
author = "Demidenko, {G. V.} and Matveeva, {I. I.}",
note = "Funding Information: This work was supported by the Russian Foundation for Basic Research (project no. 19-01-00754). Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.; 7th International Conference on Functional Differential Equations and Applications, FDEA 2019 ; Conference date: 22-08-2019 Through 27-08-2019",
year = "2021",
doi = "10.1007/978-981-16-6297-3_11",
language = "English",
isbn = "978-981-16-6296-6",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer, Cham",
pages = "145--167",
editor = "Alexander Domoshnitsky and Alexander Rasin and Seshadev Padhi",
booktitle = "Functional Differential Equations and Applications - FDEA-2019",
edition = "1",

}

RIS

TY - GEN

T1 - The Second Lyapunov Method for Time-Delay Systems

AU - Demidenko, G. V.

AU - Matveeva, I. I.

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research (project no. 19-01-00754). Publisher Copyright: © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

PY - 2021

Y1 - 2021

N2 - Some classes of systems of delay differential equations are considered. We give a review of methods for the study of the stability of solutions in the case of constant and periodic coefficients in linear terms. Special attention is paid to the development of the second Lyapunov method. A number of authors’ results for linear and nonlinear delay differential equations obtained by using various Lyapunov–Krasovskii functionals are presented. The application of discrete analogs of the constructed functionals to the study of the stability of solutions to delay difference equations is discussed.

AB - Some classes of systems of delay differential equations are considered. We give a review of methods for the study of the stability of solutions in the case of constant and periodic coefficients in linear terms. Special attention is paid to the development of the second Lyapunov method. A number of authors’ results for linear and nonlinear delay differential equations obtained by using various Lyapunov–Krasovskii functionals are presented. The application of discrete analogs of the constructed functionals to the study of the stability of solutions to delay difference equations is discussed.

KW - Estimates for solutions

KW - Exponential stability

KW - Lyapunov-Krasovskii functionals

KW - Periodic coefficients

KW - Time-delay systems

UR - http://www.scopus.com/inward/record.url?scp=85125224626&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/b1a34f1f-889e-37e0-a5cf-6fdbc6772ba5/

U2 - 10.1007/978-981-16-6297-3_11

DO - 10.1007/978-981-16-6297-3_11

M3 - Conference contribution

AN - SCOPUS:85125224626

SN - 978-981-16-6296-6

SN - 978-981-16-6299-7

T3 - Springer Proceedings in Mathematics and Statistics

SP - 145

EP - 167

BT - Functional Differential Equations and Applications - FDEA-2019

A2 - Domoshnitsky, Alexander

A2 - Rasin, Alexander

A2 - Padhi, Seshadev

PB - Springer, Cham

T2 - 7th International Conference on Functional Differential Equations and Applications, FDEA 2019

Y2 - 22 August 2019 through 27 August 2019

ER -

ID: 35590349