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Asymptotic Stability of a Class of Impulsive Delay Differential Equations

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  • G. L. Zhang
  • M. H. Song
  • M. Z. Liu

Abstract

This paper is concerned with a class of linear impulsive delay differential equations. Asymptotic stability of analytic solutions of this kind of equations is studied by the property of delay differential equations without impulsive perturbations. New numerical methods for this kind of equations are constructed. The convergence and asymptotic stability of the methods for this kind of equations are studied.

Suggested Citation

  • G. L. Zhang & M. H. Song & M. Z. Liu, 2012. "Asymptotic Stability of a Class of Impulsive Delay Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, October.
    • Handle: RePEc:hin:jnljam:723893
    DOI: 10.1155/2012/723893
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    Cited by:

    1. Zhang, Gui-Lai & Song, Ming-Hui, 2019. "Impulsive continuous Runge–Kutta methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 160-173.
    2. Rengamannar, Kaviya & Balakrishnan, Ganesh Priya & Palanisamy, Muthukumar & Niezabitowski, Michal, 2020. "Exponential stability of non-linear stochastic delay differential system with generalized delay-dependent impulsive points," Applied Mathematics and Computation, Elsevier, vol. 382(C).

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