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Asymptotic comparison of the solutions of linear time-delay systems with point and distributed lags with those of their limiting equations. (English) Zbl 1191.34096
This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of the corresponding perturbed functional differential equation. Both differential equations involve point and distributed delayed dynamics including Volterra class dynamics. The proofs are based on a Perron-type theorem for functional equations so that the comparison is governed by the real part of a dominant zero of the characteristic equation of the nominal differential equation. The obtained results are also applied to investigate the global stability of the perturbed equation based on that of its corresponding limiting equation.
MSC:
34K25Asymptotic theory of functional-differential equations
34K06Linear functional-differential equations
34K20Stability theory of functional-differential equations
34K27Perturbations of functional-differential equations