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<p>This paper investigates the problem of set-membership fault detection for Linear Time-Invariant (LTI) systems, with application to DC motors. The studied system is subject to disturbances, noise, and sensor faults, where uncertainties are assumed to be unknown but bounded within predefined sets. To address this issue, two Interval-Based Fault Detection Observers (IBFDOs) are proposed: the first follows a Luenberger observer structure, while the second employs a T-N-L structure. To enhance Fault Detection (FD) performance, an <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L_\infty\)</EquationSource> </InlineEquation> criterion is introduced for both observers to mitigate the impact of disturbances and noise. Additionally, fault sensitivity is evaluated for the T-N-L observer using the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H_ -\)</EquationSource> </InlineEquation> index, where a mixed <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(H_ - / L_\infty\)</EquationSource> </InlineEquation> performance criterion is implemented to achieve a trade-off between robustness against uncertainties and sensitivity to faults. The stability conditions, disturbance attenuation, and fault sensitivity requirements are formulated as Linear Matrix Inequalities (LMIs). The effectiveness of the proposed methods is demonstrated through case studies involving DC motors, followed by a comparative analysis to assess their ability to detect minimal faults.</p>

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Sensor Fault Detection for Linear-Time Invariant Systems Based on \(H_ -\) and \(L_\infty\) Performances: Application to DC Motors

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Haifa Ethabet,
  • Leila Dadi,
  • Mohamed Aoun,
  • Tarek Raïssi

摘要

This paper investigates the problem of set-membership fault detection for Linear Time-Invariant (LTI) systems, with application to DC motors. The studied system is subject to disturbances, noise, and sensor faults, where uncertainties are assumed to be unknown but bounded within predefined sets. To address this issue, two Interval-Based Fault Detection Observers (IBFDOs) are proposed: the first follows a Luenberger observer structure, while the second employs a T-N-L structure. To enhance Fault Detection (FD) performance, an \(L_\infty\) criterion is introduced for both observers to mitigate the impact of disturbances and noise. Additionally, fault sensitivity is evaluated for the T-N-L observer using the \(H_ -\) index, where a mixed \(H_ - / L_\infty\) performance criterion is implemented to achieve a trade-off between robustness against uncertainties and sensitivity to faults. The stability conditions, disturbance attenuation, and fault sensitivity requirements are formulated as Linear Matrix Inequalities (LMIs). The effectiveness of the proposed methods is demonstrated through case studies involving DC motors, followed by a comparative analysis to assess their ability to detect minimal faults.