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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2007, Volume 13, Number 2, Pages 66–79
(Mi timm89)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 19.10.2006
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
Linking options:
https://www.mathnet.ru/eng/timm89 https://www.mathnet.ru/eng/timm/v13/i2/p66
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