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

Author

Listed:
  • Josef Rebenda
  • Zdeněk Šmarda

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.

Suggested Citation

  • Josef Rebenda & Zdeněk Šmarda, 2013. "Stability of a Functional Differential System with a Finite Number of Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:853134
    DOI: 10.1155/2013/853134
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    References listed on IDEAS

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    1. Jaromír Baštinec & Leonid Berezansky & Josef Diblík & Zdeněk Šmarda, 2010. "On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Jaromír Baštinec & Leonid Berezansky & Josef Diblík & Zdeněk Šmarda, 2010. "On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-20, September.
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