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Fault Detection for Uncertain Fuzzy Systems Based on the Delta Operator Approach

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Abstract

This paper investigates the problem of designing a robust fault-detection for uncertain T-S fuzzy models based on the delta operator approach. By means of the T-S fuzzy delta operator systems, a fuzzy fault detection filter system is constructed via the delta operator approach. The worst case fault sensitivity has been formulated in terms of linear matrix inequalities. The proposed fault-detection filter not only ensures the H −-gain from a fault signal to a residual signal greater than a prescribed value, but also guarantees the H ∞-gain from an exogenous input to a residual signal less than a prescribed value in terms of the solvability of linear matrix inequalities. The linear matrix inequalities can be solved by an effective algorithm. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their detailed comments which helped to improve the quality of the paper. The work of Hongjiu Yang was supported by the National Natural Science Foundation of China under Grant 61203023, the Postdoctoral Science Foundation of China under Grant 2012M510769, and the Natural Science Foundation of Hebei Education Department under Grant Q2012060 and the Hebei Provincial Natural Science Fund under Grand F2013203092, and the Science Technology Research and Development Plan of Qinhuangdao City under Grant 201302A030. The work of Zhixin Liu was supported partially by the Natural Science Foundation of China under Grant 61104033, and the Hebei Provincial Natural Science Fund under Grand F2012203109. The work of Changchun Hua was supported by the Science Fund for Distinguished Young Scholars of Hebei Province (F2011203110), Doctoral Fund of Ministry of Education of China (20121333110008), the National Natural Science Foundation of China (60934003, 61290322, 61273222).

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Authors and Affiliations

  1. The Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Hongjiu Yang, Xuan Li, Zhixin Liu & Changchun Hua

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  1. Hongjiu Yang
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  2. Xuan Li
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Correspondence to Zhixin Liu.

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Yang, H., Li, X., Liu, Z. et al. Fault Detection for Uncertain Fuzzy Systems Based on the Delta Operator Approach. Circuits Syst Signal Process 33, 733–759 (2014). https://doi.org/10.1007/s00034-013-9676-2

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  • DOI: https://doi.org/10.1007/s00034-013-9676-2

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