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A Lyapunov matrix based stability criterion for a class of time-delay systems. / Gomez, Marco; Egorov, Alexey Valerievich; Mondié, Sabine A.

In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Vol. 13, No. 4, 01.01.2017, p. 407-416.

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

Harvard

Gomez, M, Egorov, AV & Mondié, SA 2017, 'A Lyapunov matrix based stability criterion for a class of time-delay systems', Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, vol. 13, no. 4, pp. 407-416. https://doi.org/10.21638/11701/spbu10.2017.407

APA

Gomez, M., Egorov, A. V., & Mondié, S. A. (2017). A Lyapunov matrix based stability criterion for a class of time-delay systems. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, 13(4), 407-416. https://doi.org/10.21638/11701/spbu10.2017.407

Vancouver

Gomez M, Egorov AV, Mondié SA. A Lyapunov matrix based stability criterion for a class of time-delay systems. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2017 Jan 1;13(4):407-416. https://doi.org/10.21638/11701/spbu10.2017.407

Author

Gomez, Marco ; Egorov, Alexey Valerievich ; Mondié, Sabine A. / A Lyapunov matrix based stability criterion for a class of time-delay systems. In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2017 ; Vol. 13, No. 4. pp. 407-416.

BibTeX

@article{2404ead596b3447689eec39eb78fe51f,
title = "A Lyapunov matrix based stability criterion for a class of time-delay systems",
abstract = "This paper is devoted to the stability analysis of linear time-invariant systems with multiple delays. First, we recover some basic elements of our research. Namely, we introduce the complete type functionals, the delay Lyapunov matrix, and a space of special functions that allow to present a family of necessary stability conditions. Then, we prove a sufficient stability condition (instability condition) in terms of a quadratic Lyapunov—Krasovskii functional. Summarizing these results, we finally obtain an exponential stability criterion for a class of linear time-delay systems. The criterion requires only a finite number of mathematical operations to be tested and depends uniquely on the delay Lyapunov matrix. Refs 15.",
keywords = "Lyapunov matrix, Stability criterion, Time-delay system",
author = "Marco Gomez and Egorov, {Alexey Valerievich} and Mondi{\'e}, {Sabine A.}",
year = "2017",
month = jan,
day = "1",
doi = "10.21638/11701/spbu10.2017.407",
language = "English",
volume = "13",
pages = "407--416",
journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",
issn = "1811-9905",
publisher = "Издательство Санкт-Петербургского университета",
number = "4",

}

RIS

TY - JOUR

T1 - A Lyapunov matrix based stability criterion for a class of time-delay systems

AU - Gomez, Marco

AU - Egorov, Alexey Valerievich

AU - Mondié, Sabine A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - This paper is devoted to the stability analysis of linear time-invariant systems with multiple delays. First, we recover some basic elements of our research. Namely, we introduce the complete type functionals, the delay Lyapunov matrix, and a space of special functions that allow to present a family of necessary stability conditions. Then, we prove a sufficient stability condition (instability condition) in terms of a quadratic Lyapunov—Krasovskii functional. Summarizing these results, we finally obtain an exponential stability criterion for a class of linear time-delay systems. The criterion requires only a finite number of mathematical operations to be tested and depends uniquely on the delay Lyapunov matrix. Refs 15.

AB - This paper is devoted to the stability analysis of linear time-invariant systems with multiple delays. First, we recover some basic elements of our research. Namely, we introduce the complete type functionals, the delay Lyapunov matrix, and a space of special functions that allow to present a family of necessary stability conditions. Then, we prove a sufficient stability condition (instability condition) in terms of a quadratic Lyapunov—Krasovskii functional. Summarizing these results, we finally obtain an exponential stability criterion for a class of linear time-delay systems. The criterion requires only a finite number of mathematical operations to be tested and depends uniquely on the delay Lyapunov matrix. Refs 15.

KW - Lyapunov matrix

KW - Stability criterion

KW - Time-delay system

UR - http://www.scopus.com/inward/record.url?scp=85040463918&partnerID=8YFLogxK

U2 - 10.21638/11701/spbu10.2017.407

DO - 10.21638/11701/spbu10.2017.407

M3 - Article

AN - SCOPUS:85040463918

VL - 13

SP - 407

EP - 416

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

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

SN - 1811-9905

IS - 4

ER -

ID: 41181311