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Intermittent boundary control for fixed-time stability of reaction–diffusion systems

Author

Listed:
  • Jia, Wenwen
  • Xie, Jingu
  • Guo, Haihua
  • Wu, Yongbao

Abstract

This work is a pilot effort to investigate the fixed-time stability (FxTS) of reaction–diffusion systems under aperiodically intermittent boundary control (AIBC). The average control rate and a new Lyapunov function are proposed to overcome the challenges of handling the FxTS of reaction–diffusion systems with AIBC. Moreover, the proposed method is applicable to the study of finite-time stability and exponential stability of reaction–diffusion systems under AIBC. Based on the Wirtinger’s inequality and the Lyapunov method, a FxTS criterion for a reaction–diffusion system with AIBC is given. Finally, two examples are discussed along with the simulated results to verify the effectiveness of the proposed method.

Suggested Citation

  • Jia, Wenwen & Xie, Jingu & Guo, Haihua & Wu, Yongbao, 2024. "Intermittent boundary control for fixed-time stability of reaction–diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s096007792400256x
    DOI: 10.1016/j.chaos.2024.114704
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    References listed on IDEAS

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    1. Cai, Shuiming & Hou, Meiyuan, 2021. "Quasi-synchronization of fractional-order heterogeneous dynamical networks via aperiodic intermittent pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Su, Haipeng & Luo, Runzi & Huang, Meichun & Fu, Jiaojiao, 2022. "Practical fixed time active control scheme for synchronization of a class of chaotic neural systems with external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Li, Xing-Yu & Wu, Kai-Ning & Liu, Xiao-Zhen, 2023. "Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    4. Mathiyalagan, K. & Renugadevi, T. & Nidhi, A. Shree & Ma, Yong-Ki & Cao, Jinde, 2022. "Boundary state feedback control for semilinear fractional-order reaction diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Panda, Sumati Kumari & Vijayakumar, Velusamy, 2023. "Results on finite time stability of various fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Shuiming Cai & Shulan Zhuang & Jinyao Shi & Peipei Zhou, 2023. "New fixed-time synchronization results for discontinuous dynamic networks: A novel two-stage analysis approach," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(11), pages 1-30, November.
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