Abstract and Applied Analysis

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

Josef Rebenda and Zdeněk Šmarda

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 853134, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449432

Digital Object Identifier
doi:10.1155/2013/853134

Mathematical Reviews number (MathSciNet)
MR3068870

Zentralblatt MATH identifier
1297.34083

Citation

Rebenda, Josef; Šmarda, Zdeněk. Stability of a Functional Differential System with a Finite Number of Delays. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 853134, 10 pages. doi:10.1155/2013/853134. https://projecteuclid.org/euclid.aaa/1393449432


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