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Finite-time stability of impulsive reaction-diffusion systems with and without time delay

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  • Wu, Kai-Ning
  • Na, Ming-Ye
  • Wang, Liming
  • Ding, Xiaohua
  • Wu, Boying

Abstract

This paper considers the finite-time stability of impulsive reaction-diffusion systems (IRDSs). We deal with two cases, systems without time delay and systems with time delay. When there is no delay in the considered system, we obtain sufficient conditions to guarantee the finite-time stability of IRDSs via two representations of impulsive sequences. When time delay enters into IRDSs, we adopt a comparison method to deal with the finite-time stability and provide sufficient conditions ensuring the finite-time stability. We also present the differences of finite-time stability and asymptotic stability for the IRDSs. Moreover, in our sufficient conditions, we show the effects of impulse, diffusion and spatial domain on the finite-time stability and discuss the effect of time delay on the stability. Numerical simulations are carried out to show the effectiveness of our obtained results.

Suggested Citation

  • Wu, Kai-Ning & Na, Ming-Ye & Wang, Liming & Ding, Xiaohua & Wu, Boying, 2019. "Finite-time stability of impulsive reaction-diffusion systems with and without time delay," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:15
    DOI: 10.1016/j.amc.2019.124591
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    1. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    2. Wang, Zhen & Xie, Yingkang & Lu, Junwei & Li, Yuxia, 2019. "Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 360-369.
    3. R. Saravanakumar & M. Syed Ali & H. R. Karimi, 2017. "Robust control of uncertain stochastic Markovian jump systems with mixed time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 862-872, March.
    4. Hao Liu & Peng Shi & Hamid Reza Karimi & Mohammed Chadli, 2016. "Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1433-1444, April.
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    Cited by:

    1. You, Luyao & Yang, Xueyan & Wu, Shuchen & Li, Xiaodi, 2023. "Finite-time stabilization for uncertain nonlinear systems with impulsive disturbance via aperiodic intermittent control," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    2. Du, Haibo & Yu, Bo & Wei, Jiajia & Zhang, Jun & Wu, Di & Tao, Weiqing, 2020. "Attitude trajectory planning and attitude control for quad-rotor aircraft based on finite-time control technique," Applied Mathematics and Computation, Elsevier, vol. 386(C).

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