Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations | Zendy

Manuel De la Sen | Zendy

Open Access

Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations

Author(s) -

Manuel De la Sen

Publication year - 2009

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2009/216746

Subject(s) - mathematics , differential equation , delay differential equation , limiting , mathematical analysis , homogeneous differential equation , first order partial differential equation , functional differential equation , exponential stability , exact differential equation , mathematical proof , linear differential equation , stability (learning theory) , functional equation , nonlinear system , differential algebraic equation , ordinary differential equation , mechanical engineering , physics , geometry , quantum mechanics , machine learning , computer science , engineering

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

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