Fault Detection Observer Design for Nonlinear Systems via Fuzzy Lyapunov Functions

This article focuses on the design problem of fault detection (FD) observer for a class of continuous-time nonlinear systems. The \mathcal {H_{-}} index is employed to measure the worst cast fault sensitivity. First, the nonlinear systems are represented by the Takagi-Sugeno (T-S) fuzzy dynamic mo...

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Bibliographic Details
Published in:IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2022-10, Vol.52 (10), p.6607-6617
Main Authors: Liu, Guo-Jun, Chang, Xiao-Heng, Park, Ju H., Hu, Mengjie
Format: Article
Language:English
Subjects:
Analytical models
Control systems
Dynamic models
Fault detection
fault detection (FD)
fuzzy Lyapunov functions (FLFs)
Fuzzy systems
H_index
Indexes
Liapunov functions
Linear matrix inequalities
Lyapunov methods
Mathematical analysis
Nonlinear systems
Observers
Stability analysis
Takagi–Sugeno (T–S) fuzzy systems
Upper bounds
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Summary:This article focuses on the design problem of fault detection (FD) observer for a class of continuous-time nonlinear systems. The \mathcal {H_{-}} index is employed to measure the worst cast fault sensitivity. First, the nonlinear systems are represented by the Takagi-Sugeno (T-S) fuzzy dynamic models. Then, a novel fuzzy Lyapunov function (FLF) analyzing approach is proposed to reduce the conservatism in stability analysis and \mathcal {H_{-}} index estimation for the T-S fuzzy model. In particular, employing this new type of the FLF, the stability analysis of the T-S fuzzy systems perfectly overcomes the difficulty of evaluating the upper bound of the time derivative of the membership function. Based on the descriptor system approach, some new sufficient conditions on the existence of fuzzy FD observers are obtained in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness of the proposed method.
ISSN:2168-2216
2168-2232
DOI:10.1109/TSMC.2022.3147459