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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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    5. 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).
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