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Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique

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  • Shiguo Peng
  • Liping Yang

Abstract

This paper develops some new Razumikhin‐type theorems on global exponential stability of impulsive functional differential equations. Some applications are given to impulsive delay differential equations. Compared with some existing works, a distinctive feature of this paper is to address exponential stability problems for any finite delay. It is shown that the functional differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. Two examples verify the effectiveness of the proposed results.

Suggested Citation

  • Shiguo Peng & Liping Yang, 2010. "Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:987372
    DOI: 10.1155/2010/987372
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    Cited by:

    1. Pei Cheng & Zheng Wu & Lianglong Wang, 2012. "New Results on Global Exponential Stability of Impulsive Functional Differential Systems with Delayed Impulses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. X. J. Wan & Y. P. Zhang & J. T. Sun, 2013. "Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Exponential Stability of Impulsive Stochastic Functional Differential Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    5. L. J. Shen & J. T. Sun, 2011. "Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).

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