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Robust fault reconstruction for a class of non-infinitely observable descriptor systems using two sliding mode observers in cascade

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  • Chan, Joseph Chang Lun
  • Tan, Chee Pin
  • Trinh, Hieu
  • Kamal, Md Abdus Samad
  • Chiew, Yeong Shiong

Abstract

Existing sliding mode observer (SMO) schemes for fault reconstruction in descriptor systems require stringent conditions, or do not consider disturbances which can corrupt the reconstruction. In this paper, we present a two-observer scheme that overcomes these limitations by treating certain states as unknown inputs, thereby formulating a reduced-order infinitely observable system. A SMO is implemented onto this system to reconstruct certain faults, and its switching feedback term is fed into another SMO to reconstruct the remaining faults. Linear matrix inequalities (LMIs) are used to design observer gains in order to minimise the L2 gain of the disturbances on the fault reconstruction. The existence conditions of the scheme are investigated and are found to be less restrictive than those from other schemes in the literature, and thus the scheme is applicable to a wider class of systems compared to existing schemes. Finally, a simulation example demonstrates the efficacy of the proposed scheme.

Suggested Citation

  • Chan, Joseph Chang Lun & Tan, Chee Pin & Trinh, Hieu & Kamal, Md Abdus Samad & Chiew, Yeong Shiong, 2019. "Robust fault reconstruction for a class of non-infinitely observable descriptor systems using two sliding mode observers in cascade," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 78-92.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:78-92
    DOI: 10.1016/j.amc.2018.12.071
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    References listed on IDEAS

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    1. Du, Dongsheng, 2017. "Fault detection for discrete-time linear systems based on descriptor observer approach," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 575-585.
    2. Liu, Yangfan & Ma, Yuechao & Wang, Yanning, 2018. "Reliable finite-time sliding-mode control for singular time-delay system with sensor faults and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 341-357.
    3. Liu, Zhen & Gao, Cunchen & Kao, Yonggui, 2015. "Robust H-infinity control for a class of neutral-type systems via sliding mode observer," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 669-681.
    4. Li, Rongchang & Zhang, Qingling, 2018. "Robust H∞ sliding mode observer design for a class of Takagi–Sugeno fuzzy descriptor systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 158-178.
    5. Joseph Chang Lun Chan & Chee Pin Tan & Hieu Trinh, 2017. "Robust fault reconstruction for a class of infinitely unobservable descriptor systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(8), pages 1646-1655, June.
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    Cited by:

    1. Lun Chan, Joseph Chang & Lee, Tae H., 2022. "Observer-based fault-tolerant control for non-infinitely observable descriptor systems with unknown time-varying state and input delays," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Sun, Yuchen & Ma, Shuping, 2021. "Output regulation of switched singular systems based on extended state observer approach," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    3. Han, Jian & Liu, Xiuhua & Wei, Xinjiang & Zhang, Huifeng & Hu, Xin, 2021. "Adjustable dimension descriptor observer based fault estimation of nonlinear system with unknown input," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. Nguyen, Cuong M. & Tan, Chee Pin & Trinh, Hieu, 2021. "State and delay reconstruction for nonlinear systems with input delays," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    5. Che, Haochi & Huang, Jun & Zhao, Xudong & Ma, Xiang & Xu, Ning, 2020. "Functional interval observer for discrete-time systems with disturbances," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    6. Jin, Xiaozheng & Tong, Xingcheng & Chi, Jing & Wu, Xiaoming & Wang, Hai, 2024. "Nonlinear estimator-based funnel tracking control for a class of perturbed Euler-Lagrange systems," Applied Mathematics and Computation, Elsevier, vol. 471(C).

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