Geodesic
Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 66-79

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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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     title = {Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay},
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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 66-79. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a5/