@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",
}