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<p>A novel geometric fault detection and isolation (FDI) method is established for fuzzy Markov jump systems (FMJS) in this paper. Firstly, the concept of a fuzzy finite unobservable subspace is proposed for FMJS. Then, by leveraging the geometric properties of factor spaces and canonical projections, distinct faults are mapped to separate unobservable subspaces. A set of reduced-order observers corresponding to the faults is further obtained, along with a set of structured residual generators that are sensitive exclusively to specific faults. Furthermore, based on Lyapunov theory, the influence of disturbances is suppressed by ensuring the stochastic stability and strict dissipativity of the system. The parameter matrices of the residual generators are determined by solving linear matrix inequalities (LMI). It is shown that the proposed method can exhibit superior sensitivity to faults and achieve easier fault decoupling compared to existing literature. Finally, the numerical simulations including a single-link robotic arm system and comparative experiments are given to demonstrate the effectiveness and robustness of our method.</p>

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Robust fault detection and isolation for fuzzy Markov jump systems based on geometric approach

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Yandong Hou,
  • Fujun Wang,
  • Zhengquan Chen,
  • Zhiheng Zhang,
  • Jiayuan Yan

摘要

A novel geometric fault detection and isolation (FDI) method is established for fuzzy Markov jump systems (FMJS) in this paper. Firstly, the concept of a fuzzy finite unobservable subspace is proposed for FMJS. Then, by leveraging the geometric properties of factor spaces and canonical projections, distinct faults are mapped to separate unobservable subspaces. A set of reduced-order observers corresponding to the faults is further obtained, along with a set of structured residual generators that are sensitive exclusively to specific faults. Furthermore, based on Lyapunov theory, the influence of disturbances is suppressed by ensuring the stochastic stability and strict dissipativity of the system. The parameter matrices of the residual generators are determined by solving linear matrix inequalities (LMI). It is shown that the proposed method can exhibit superior sensitivity to faults and achieve easier fault decoupling compared to existing literature. Finally, the numerical simulations including a single-link robotic arm system and comparative experiments are given to demonstrate the effectiveness and robustness of our method.