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Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay

Author

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  • Xiaodi Li

    (School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, China)

  • A. Vinodkumar

    (Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641 112, India)

  • T. Senthilkumar

    (Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641 112, India)

Abstract

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stability results for RIIDDS by using the Lyapunov function and Razumikhin technique. Unlike other studies, we show that the stability behavior of the random time impulses is faster than the fixed time impulses. Finally, two examples were studied for comparative results of fixed and random time impulses it shows by simulation.

Suggested Citation

  • Xiaodi Li & A. Vinodkumar & T. Senthilkumar, 2019. "Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay," Mathematics, MDPI, vol. 7(9), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:843-:d:266695
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    References listed on IDEAS

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    1. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    2. Caraballo, Tomás & Cortés, J.-C. & Navarro-Quiles, A., 2019. "Applying the random variable transformation method to solve a class of random linear differential equation with discrete delay," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 198-218.
    3. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
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    Cited by:

    1. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.

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