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Trudy Inst. Mat. i Mekh. UrO RAN, 2006, Volume 12, Number 2, Pages 78–87 (Mi timm153)  

This article is cited in 3 scientific papers (total in 3 papers)

Application of self-adjoint boundary value problems to investigation of stability of periodic delay systems

Yu. F. Dolgii


Abstract: The problem on determining conditions for the asymptotic stability of linear periodic delay systems is considered. Solving this problem, we use the function space of states. Conditions for the asymptotic stability are determined in terms of the spectrum of the monodromy operator. To find the spectrum, we construct a special boundary value problem for ordinary differential equations. The motion of eigenvalues of this problem is studied as the parameter changes. Conditions of the stability of the linear periodic delay system change when an eigenvalue of the boundary value problem intersects the circumference of the unit disk. We assume that, at this moment, the boundary value problem is self-adjoint. Sufficient coefficient conditions for the asymptotic stability of linear periodic delay systems are given.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2006, 255, suppl. 2, S16–S25

Bibliographic databases:

UDC: 517.929
Received: 23.05.2006

Citation: Yu. F. Dolgii, “Application of self-adjoint boundary value problems to investigation of stability of periodic delay systems”, Control, stability, and inverse problems of dynamics, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 2, 2006, 78–87; Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S16–S25

Citation in format AMSBIB
\Bibitem{Dol06}
\by Yu.~F.~Dolgii
\paper Application of self-adjoint boundary value problems to investigation of stability of periodic delay systems
\inbook Control, stability, and inverse problems of dynamics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 2
\pages 78--87
\mathnet{http://mi.mathnet.ru/timm153}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338472}
\zmath{https://zbmath.org/?q=an:1130.34049}
\elib{http://elibrary.ru/item.asp?id=12040738}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 255
\issue , suppl. 2
\pages S16--S25
\crossref{https://doi.org/10.1134/S0081543806060022}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33847001296}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. F. Dolgii, E. V. Ul'yanov, “Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S95–S110  mathnet  crossref  elib
    2. B. P. Lampe, E. N. Rosenwasser, “Stability investigation for linear periodic time-delayed systems using Fredholm theory”, Autom. Remote Control, 72:1 (2011), 38–60  mathnet  crossref  mathscinet  zmath  isi
    3. Qesmi R., “A Short Survey on Delay Differential Systems With Periodic Coefficients”, J. Appl. Anal. Comput., 8:1 (2018), 296–330  crossref  mathscinet  isi  scopus
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