Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2017, Volume 13, Issue 4, Pages 407–416
DOI: https://doi.org/10.21638/11701/spbu10.2017.407
(Mi vspui349)
 

This article is cited in 2 scientific papers (total in 2 papers)

Control processes

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

M. Gomeza, A. V. Egorovb, S. Mondiéa

a CINVESTAV-IPN, 2508, Av. Instituto Politécnico Nacional, Mexico city, 07360, United Mexican States
b St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (380 kB) Citations (2)
References:
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: time-delay system, Lyapunov matrix, stability criterion.
Funding agency Grant number
CONACYT - Consejo Nacional de Ciencia y Tecnología 180725
Russian Foundation for Basic Research 16-31-00436_мол_a
This work was supported by Project CONACYT N 180725 and by Russian Foundation for Basic Research (RFBR), research project N 16-31-00436 мол_a.
Received: September 2, 2017
Accepted: October 12, 2017
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: English
Citation: M. Gomez, A. V. Egorov, S. Mondié, “A Lyapunov matrix based stability criterion for a class of time-delay systems”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 13:4 (2017), 407–416
Citation in format AMSBIB
\Bibitem{GomEgoMon17}
\by M.~Gomez, A.~V.~Egorov, S.~Mondi\'e
\paper A Lyapunov matrix based stability criterion for a class of time-delay systems
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2017
\vol 13
\issue 4
\pages 407--416
\mathnet{http://mi.mathnet.ru/vspui349}
\crossref{https://doi.org/10.21638/11701/spbu10.2017.407}
\elib{https://elibrary.ru/item.asp?id=32358360}
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  • https://www.mathnet.ru/eng/vspui/v13/i4/p407
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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    Abstract page:170
    Full-text PDF :34
    References:33
    First page:13
     
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