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\(H_{-} / H_{\infty }\) Fault Detection Observer Design for Switched Singular Systems with Persistent Dwell Time

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Abstract

This paper deals with the fault detection observer (FDO) design for discrete-time switched singular systems (SSSs) under persistent dwell time (PDT) switching. Compared to the widely used dwell time and average dwell time switching in the literature, PDT switching is more general due to its covering such two switchings as special cases. The PDT switching is firstly employed to establish the admissibility criterion and the \(H_{\infty }\) and \(H_{-}\) observer synthesis conditions for SSSs. Also, an efficient \(H_{-} / H_{\infty }\) FDO design algorithm is proposed. First, the admissibility analysis of the observing error system is addressed by incorporating the PDT technique into the multiple Lyapunov function method, and an admissibility criterion in the form of linear matrix inequality is established. Based on this, two FDO synthesis conditions are then developed to guarantee that the generated residual signal achieves prescribed \(H_{\infty }\) and \(H_{-}\) performance with regard to disturbances and faults, respectively. The FDO should be designed such that the effects of faults and disturbances on the residual signal are maximized and minimized, respectively. To this end, the FDO design is expressed as a multi-objective optimization problem, and the FDO gains are characterized in terms of the solution of the multi-objective optimization problem. Moreover, a suitable trade-off between the robustness to disturbances and the sensitivity to faults is obtained based on a corresponding proposed algorithm. Finally, one illustrative example is given to show the validity of the developed method.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Authors and Affiliations

  1. School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China

    Yuanyu Zheng & Yanhui Tong

  2. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

    Bixuan Huang

  3. School of Mechatronics Engineering and Automation, Shanghai University, Shanghai, China

    Yueying Wang

Authors
  1. Yuanyu Zheng
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  2. Yanhui Tong
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  3. Bixuan Huang
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  4. Yueying Wang
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Correspondence to Yanhui Tong.

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Zheng, Y., Tong, Y., Huang, B. et al. \(H_{-} / H_{\infty }\) Fault Detection Observer Design for Switched Singular Systems with Persistent Dwell Time. Circuits Syst Signal Process 43, 2829–2852 (2024). https://doi.org/10.1007/s00034-024-02612-6

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