On the robustness and estimation of the attraction region for a class of nonlinear time delay systems

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On the robustness and estimation of the attraction region for a class of nonlinear time delay systems. / Alexandrova, Irina V.

In: Applied Mathematics Letters, Vol. 106, 106374, 08.2020.

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

BibTeX

@article{ded5fa7c89d84b70bc45101ac1444680,

title = "On the robustness and estimation of the attraction region for a class of nonlinear time delay systems",

abstract = "A new Lyapunov matrix based approach to the robustness analysis developed in recent years for linear time delay systems is nontrivially extended to address some problems of nonlinear analysis. In particular, the asymptotic stability condition for a quasilinear system is derived, as well as attraction region for a class of nonlinear time delay systems with exponentially stable linear approximation is estimated. A peculiarity of the approach is that the negative definiteness condition for the derivative of the nominal functional along the solutions of a nonlinear system is replaced with just negativeness of an “infinite” part of the integral of this derivative.",

keywords = "Asymptotic stability, Attraction region, Lyapunov matrix, Lyapunov–Krasovskii functionals, Time delay systems, LINEAR-SYSTEMS, MATRIX, STABILITY ANALYSIS, Lyapunov-Krasovskii functionals",

author = "Alexandrova, {Irina V.}",

year = "2020",

month = aug,

doi = "10.1016/j.aml.2020.106374",

language = "English",

volume = "106",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On the robustness and estimation of the attraction region for a class of nonlinear time delay systems

AU - Alexandrova, Irina V.

PY - 2020/8

Y1 - 2020/8

N2 - A new Lyapunov matrix based approach to the robustness analysis developed in recent years for linear time delay systems is nontrivially extended to address some problems of nonlinear analysis. In particular, the asymptotic stability condition for a quasilinear system is derived, as well as attraction region for a class of nonlinear time delay systems with exponentially stable linear approximation is estimated. A peculiarity of the approach is that the negative definiteness condition for the derivative of the nominal functional along the solutions of a nonlinear system is replaced with just negativeness of an “infinite” part of the integral of this derivative.

AB - A new Lyapunov matrix based approach to the robustness analysis developed in recent years for linear time delay systems is nontrivially extended to address some problems of nonlinear analysis. In particular, the asymptotic stability condition for a quasilinear system is derived, as well as attraction region for a class of nonlinear time delay systems with exponentially stable linear approximation is estimated. A peculiarity of the approach is that the negative definiteness condition for the derivative of the nominal functional along the solutions of a nonlinear system is replaced with just negativeness of an “infinite” part of the integral of this derivative.

KW - Asymptotic stability

KW - Attraction region

KW - Lyapunov matrix

KW - Lyapunov–Krasovskii functionals

KW - Time delay systems

KW - LINEAR-SYSTEMS

KW - MATRIX

KW - STABILITY ANALYSIS

KW - Lyapunov-Krasovskii functionals

UR - http://www.scopus.com/inward/record.url?scp=85082999764&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/9d67437d-270c-33bd-aa4e-37ceff71927a/

U2 - 10.1016/j.aml.2020.106374

DO - 10.1016/j.aml.2020.106374

M3 - Article

AN - SCOPUS:85082999764

VL - 106

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

M1 - 106374

ER -

ID: 61461992