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 Trudy Inst. Mat. i Mekh. UrO RAN, 2007, Volume 13, Number 2, Pages 66–79 (Mi timm89)

Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay

Yu. F. Dolgii, E. V. Ul'yanov

Abstract: To obtain sufficient conditions for the asymptotic stability of linear periodic systems with fixed delay commensurable with the period of coefficients, singular numbers of the monodromy operator are used. To find these numbers, a self-adjoint boundary value problem for ordinary differential equations is applied. We study the motion of eigenvalues of this boundary value problem under a variation of a parameter. Obtaining sufficient conditions for the asymptotic stability is reduced to finding the bifurcation value of the parameter for the boundary value problem.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2007, 259, suppl. 2, S95–S110

UDC: 517.929

Citation: 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”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 2, 2007, 66–79; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S95–S110

Citation in format AMSBIB
\Bibitem{DolUly07} \by Yu.~F.~Dolgii, E.~V.~Ul'yanov \paper Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2007 \vol 13 \issue 2 \pages 66--79 \mathnet{http://mi.mathnet.ru/timm89} \elib{http://elibrary.ru/item.asp?id=12040769} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2007 \vol 259 \issue , suppl. 2 \pages S95--S110 \crossref{https://doi.org/10.1134/S0081543807060065} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38949158510} 

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This publication is cited in the following articles:
1. 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
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