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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 853134, 10 pages
http://dx.doi.org/10.1155/2013/853134
Research Article

Stability of a Functional Differential System with a Finite Number of Delays

1CEITEC BUT, Brno University of Technology, Technicka 3058/10, 61600 Brno, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 8, 61600 Brno, Czech Republic

Received 22 December 2012; Accepted 23 May 2013

Academic Editor: Zhiming Guo

Copyright © 2013 Josef Rebenda and Zdeněk Šmarda. 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

The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.