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Boundary state and output feedback stabilisation of a coupled time fractional hyperbolic equation

Author

Listed:
  • Chunwan Lv
  • Chufen Wu
  • Ze-Hao Wu
  • Da-Yan Liu

Abstract

In this paper, the boundary stabilisation of a coupled time fractional hyperbolic equation system is investigated by both state and output feedback. A target system is first introduced, which, by the semigroup method and the Lyapunov one, is proved to admit a unique solution and is Mittag–Leffler stable. A boundary state feedback controller and state observer are designed via the backstepping technique, with explicit formulae for the gain functions. An observer-based output feedback stabilising controller is then proposed for the controlled system. Some rigorous theoretical proofs are given to demonstrate that the resulting closed-loop system under the state and output feedback controllers has a unique solution and is Mittag–Leffler stable. Some numerical simulations are performed to validate the effectiveness of the proposed control approach.

Suggested Citation

  • Chunwan Lv & Chufen Wu & Ze-Hao Wu & Da-Yan Liu, 2023. "Boundary state and output feedback stabilisation of a coupled time fractional hyperbolic equation," International Journal of Systems Science, Taylor & Francis Journals, vol. 54(11), pages 2366-2381, August.
    • Handle: RePEc:taf:tsysxx:v:54:y:2023:i:11:p:2366-2381
    DOI: 10.1080/00207721.2023.2230464
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