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Volume 8 Issue 6
Jun.  2021

IEEE/CAA Journal of Automatica Sinica

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Zhixiong Zhong, Xingyi Wang and Hak-Keung Lam, "Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1141-1152, June 2021. doi: 10.1109/JAS.2021.1004024
Citation: Zhixiong Zhong, Xingyi Wang and Hak-Keung Lam, "Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1141-1152, June 2021. doi: 10.1109/JAS.2021.1004024

Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

doi: 10.1109/JAS.2021.1004024
Funds:  This work was supported in part by the Central Government Drects Special Funds for Scientific and Technological Development of China (2019L3009), and Natural Science Foundation of Fujian Province of China (2020J02045)
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  • This article addresses the finite-time boundedness (FTB) problem for nonlinear descriptor systems. Firstly, the nonlinear descriptor system is represented by the Takagi-Sugeno (T-S) model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into a linear one. Then, we introduce a fuzzy sliding mode control (FSMC) law, which ensures the finite-time boundedness (FTB) of closed-loop fuzzy control systems over the reaching phase and sliding motion phase. Moreover, by further employing the descriptor redundancy representation, the sufficient condition for designing FSMC law, which ensures the FTB of the closed-loop control systems over the entire finite-time interval, is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study with control of a photovoltaic (PV) nonlinear system is given to show the effectiveness of the proposed method.

     

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    Highlights

    • By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix of system is reformulated into the linear one.
    • For a specified time interval, partition with transient dynamics of sliding mode control into two subintervals: Reaching phase and sliding motion phase.
    • Based on the Lyapunov function in the descriptor system domain, the design of FSMC Law is derived in terms of LMIs.

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