Abstract and Applied Analysis
Volume 2009 (2009), Article ID 216746, 37 pages
doi:10.1155/2009/216746
Research Article

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

M. De la Sen

Department of Electricity and Electronics, Faculty of Science and Technology, Institute of Research and Development of Processes (IIDP), Leioa (Bizkaia), P.O. Box. 644, 48080 Bilbao, Spain

Received 25 November 2008; Accepted 6 February 2009

Academic Editor: John Rassias

Copyright © 2009 M. De la Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.