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Asymptotic stabilisation of coupled delayed time fractional reaction diffusion systems with boundary input disturbances via backstepping sliding-mode control

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  • Juan Chen
  • Bo Zhuang
  • Yajuan Yu

Abstract

In this paper we study the asymptotic stabilisation for coupled time fractional reaction diffusion (FRD) systems with time varying delays and input disturbances by backstepping-based boundary sliding-mode control. Here, the spatially varying diffusion coefficients can be same or distinct. To stabilise the system, we first use an invertible backstepping transformation to convert an original dynamics into a target dynamics with new manipulable inputs and perturbations. Then, we employ the sliding-mode algorithm to design this discontinuous controller to suppress disturbances. In this case, we obtain the combined backstepping/sliding-mode controller of the original dynamics. By using the fractional Halanay's inequality, the delay-independent stability condition is obtained for the asymptotic stabilisation of the delayed target system and therefore of the delayed original system under the combined controller. Fractional numerical examples are given to verify the efficiency of the proposed synthesis.

Suggested Citation

  • Juan Chen & Bo Zhuang & Yajuan Yu, 2022. "Asymptotic stabilisation of coupled delayed time fractional reaction diffusion systems with boundary input disturbances via backstepping sliding-mode control," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(14), pages 3112-3130, October.
    • Handle: RePEc:taf:tsysxx:v:53:y:2022:i:14:p:3112-3130
    DOI: 10.1080/00207721.2022.2074567
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    Cited by:

    1. Chen, Juan & Zhou, Hua-Cheng & Zhuang, Bo & Xu, Ming-Hua, 2023. "Active disturbance rejection control to stabilization of coupled delayed time fractional-order reaction–advection–diffusion systems with boundary disturbances and spatially varying coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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