Necessary stability conditions for linear systems with incommensurate delays

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Necessary stability conditions for linear systems with incommensurate delays. / Alexandrova, Irina V.; Mondié, Sabine.

In: Automatica, Vol. 129, 109628, 01.07.2021.

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

BibTeX

@article{afd91dd2054c4a41a5479db1c72e4ad2,

title = "Necessary stability conditions for linear systems with incommensurate delays",

abstract = "The Lyapunov matrix is a key element of the construction of Lyapunov–Krasovskii functionals with prescribed derivative for linear time-invariant time delay systems. Moreover, stability criteria which are based exclusively on the Lyapunov matrix have been developed recently. A weak point of the approach is a lack of effective techniques to compute the Lyapunov matrix when the delays are incommensurate, i.e. at least two of them are rationally independent. To overcome this difficulty, we present in this paper necessary stability conditions for systems with incommensurate delays based on the Lyapunov matrix of a “close” auxiliary system with commensurate delays, which can be computed by known techniques. An explicit condition for the choice of delays of the auxiliary system is provided. Illustrative examples are given.",

keywords = "Incommensurate delays, Linear time-invariant (LTI) systems, Lyapunov matrix, Lyapunov–Krasovskii functionals, Stability, Time delay, Lyapunov-Krasovskii functionals",

author = "Alexandrova, {Irina V.} and Sabine Mondi{\'e}",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2021",

month = jul,

day = "1",

doi = "10.1016/j.automatica.2021.109628",

language = "English",

volume = "129",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Necessary stability conditions for linear systems with incommensurate delays

AU - Alexandrova, Irina V.

AU - Mondié, Sabine

PY - 2021/7/1

Y1 - 2021/7/1

N2 - The Lyapunov matrix is a key element of the construction of Lyapunov–Krasovskii functionals with prescribed derivative for linear time-invariant time delay systems. Moreover, stability criteria which are based exclusively on the Lyapunov matrix have been developed recently. A weak point of the approach is a lack of effective techniques to compute the Lyapunov matrix when the delays are incommensurate, i.e. at least two of them are rationally independent. To overcome this difficulty, we present in this paper necessary stability conditions for systems with incommensurate delays based on the Lyapunov matrix of a “close” auxiliary system with commensurate delays, which can be computed by known techniques. An explicit condition for the choice of delays of the auxiliary system is provided. Illustrative examples are given.

AB - The Lyapunov matrix is a key element of the construction of Lyapunov–Krasovskii functionals with prescribed derivative for linear time-invariant time delay systems. Moreover, stability criteria which are based exclusively on the Lyapunov matrix have been developed recently. A weak point of the approach is a lack of effective techniques to compute the Lyapunov matrix when the delays are incommensurate, i.e. at least two of them are rationally independent. To overcome this difficulty, we present in this paper necessary stability conditions for systems with incommensurate delays based on the Lyapunov matrix of a “close” auxiliary system with commensurate delays, which can be computed by known techniques. An explicit condition for the choice of delays of the auxiliary system is provided. Illustrative examples are given.

KW - Incommensurate delays

KW - Linear time-invariant (LTI) systems

KW - Lyapunov matrix

KW - Lyapunov–Krasovskii functionals

KW - Stability

KW - Time delay

KW - Lyapunov-Krasovskii functionals

UR - http://www.scopus.com/inward/record.url?scp=85103794014&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/c93d961b-29b3-392b-90cb-3767d751cf25/

U2 - 10.1016/j.automatica.2021.109628

DO - 10.1016/j.automatica.2021.109628

M3 - Article

AN - SCOPUS:85103794014

VL - 129

JO - Automatica

JF - Automatica

SN - 0005-1098

M1 - 109628

ER -

ID: 85683663