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<p>This study aims to deal with the problem of designing stubborn state observers for a class of nonlinear descriptor systems subject to possible external disturbances and unexpected measurement outliers. Nonlinear terms, in particular, meet the condition of incremental quadratic constraints that can describe a wide range of nonlinearities. A stubborn state observer is developed by injecting saturated output error with an adaptive saturation level to effectively attenuate the adverse impact of measurement outliers. Then, an appropriate Lyapunov function is established, and some sufficient conditions expressed by linear matrix inequalities are obtained to ensure that the estimation error system can achieve exponential admissibility with the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> </InlineEquation> performance requirement. Finally, the availability of the proposed observer is validated using two practical examples.</p>

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Stubborn State Observers for Incrementally Quadratic Descriptor Systems Subject to Measurement Outliers

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Leipo Liu,
  • Qiaofeng Wen,
  • Yanan Li,
  • Dexin Fu,
  • Xiushan Cai

摘要

This study aims to deal with the problem of designing stubborn state observers for a class of nonlinear descriptor systems subject to possible external disturbances and unexpected measurement outliers. Nonlinear terms, in particular, meet the condition of incremental quadratic constraints that can describe a wide range of nonlinearities. A stubborn state observer is developed by injecting saturated output error with an adaptive saturation level to effectively attenuate the adverse impact of measurement outliers. Then, an appropriate Lyapunov function is established, and some sufficient conditions expressed by linear matrix inequalities are obtained to ensure that the estimation error system can achieve exponential admissibility with the \(H_{\infty }\) performance requirement. Finally, the availability of the proposed observer is validated using two practical examples.