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\(H_\infty \) Fault Detection for Discrete-Time Hybrid Systems via a Descriptor System Method

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Abstract

This paper solves the problem of fault detection for discrete-time hybrid systems via a descriptor system method. These systems include control inputs, unknown bounded disturbances, and sensor faults. Based on the descriptor system method, a fault detection observer is designed to obtain the estimation of the states, outputs and faults, simultaneously. By means of the observer gain, the state error system is stochastically stable, and the disturbances effect on the residuals meets the \(H_\infty \) performance index. The satisfactory sensitivity problem of the residuals to the faults is solved. A numerical example illustrates the effectiveness and applicability of the developed method.

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Acknowledgments

The authors would like to thank the referees for their valuable and helpful comments which have improved the presentation. The work was supported by the National Basic Research Program of China (973 Program) (2012CB720000), the National Natural Science Foundation of China (61225015), Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 61321002 ), the Ph.D. Programs Foundation of Ministry of Education of China (20111101110012), and CAST Foundation (CAST201210).

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Authors and Affiliations

  1. School of Automation, Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology, Beijing, 100081, China

    Xiaodan Zhu, Yuanqing Xia & Meiling Wang

  2. Institute of Ordnance Technology, Ordnance Engineering College, Shijiazhuang, 050000, China

    Sasa Ma

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  1. Xiaodan Zhu
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  2. Yuanqing Xia
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  4. Sasa Ma
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Correspondence to Yuanqing Xia.

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Zhu, X., Xia, Y., Wang, M. et al. \(H_\infty \) Fault Detection for Discrete-Time Hybrid Systems via a Descriptor System Method. Circuits Syst Signal Process 33, 2807–2826 (2014). https://doi.org/10.1007/s00034-014-9779-4

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  • DOI: https://doi.org/10.1007/s00034-014-9779-4

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