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<p>This paper investigates the fault estimation (FE) problem for singularly perturbed Takagi-Sugeno (T-S) fuzzy systems subject to actuator faults and external disturbances. First, an intermediate observer is designed to estimate actuator faults. To address the non-convex issue arising from the fuzzy Lyapunov function (FLF) method, a novel nonlinear compensation strategy in the consequent part of the observer is proposed by fully utilizing the information of the time derivatives of membership functions (TDMFs). Specifically, by introducing a nonlinear compensation term, the TDMFs-dependent non-convex term in the observer design conditions is eliminated, making the design conditions solvable. Furthermore, to enhance the robustness of FE, the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11844_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> performance of the observer is analyzed, and the corresponding design conditions are derived. Unlike existing methods that address the non-convex problem by imposing local regional restrictions on system states or introducing dwell-time constraints, the proposed nonlinear compensation scheme resolves the issue without adding the aforementioned constraints, thereby reducing conservatism. Finally, the effectiveness of the proposed method is validated through a simulation example.</p>

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Fault estimation for singularly perturbed T-S fuzzy systems based on the \(L_{\infty }\) observer with a novel nonlinear compensation scheme

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Shanfeng Zhang,
  • Yue Wu,
  • Jiuxiang Dong

摘要

This paper investigates the fault estimation (FE) problem for singularly perturbed Takagi-Sugeno (T-S) fuzzy systems subject to actuator faults and external disturbances. First, an intermediate observer is designed to estimate actuator faults. To address the non-convex issue arising from the fuzzy Lyapunov function (FLF) method, a novel nonlinear compensation strategy in the consequent part of the observer is proposed by fully utilizing the information of the time derivatives of membership functions (TDMFs). Specifically, by introducing a nonlinear compensation term, the TDMFs-dependent non-convex term in the observer design conditions is eliminated, making the design conditions solvable. Furthermore, to enhance the robustness of FE, the \(L_{\infty }\) L ∞ performance of the observer is analyzed, and the corresponding design conditions are derived. Unlike existing methods that address the non-convex problem by imposing local regional restrictions on system states or introducing dwell-time constraints, the proposed nonlinear compensation scheme resolves the issue without adding the aforementioned constraints, thereby reducing conservatism. Finally, the effectiveness of the proposed method is validated through a simulation example.