Robust Fault Detection for Uncertain T–S Fuzzy System with Unmeasurable Premise Variables: Descriptor Approach

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Abstract

This paper considers the design of robust observer for nonlinear uncertain systems affected by sensor fault and subject to external disturbance, represented under the multiple fuzzy model formulation of Takagi–Sugeno with unmeasurable premise variables. Using the technique of descriptor system which considers sensor faults as an auxiliary state variable, we proposed a new less conservative approach in terms of a linear matrix inequality based on Lyapunov theory and \(H_{\infty }\) performance to established sufficient conditions for the existence of the considered observer. The observer estimates the previous mentioned variables and attenuates the effect of the modeling uncertainties and the perturbations on the estimation error. The benefits of the proposed approach regarding the classical one are shown through an academic example. An application to a reduced bioreactor model is considered, and the performances of the proposed approach are illustrated through numerical results.

Keywords

T–S fuzzy models Observer Sensor faults Descriptor approach Modeling uncertainties Disturbance \(H_{\infty }\) performance LMI 

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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Imen Haj Brahim
    • 1
  • Driss Mehdi
    • 2
  • Mohamed Chaabane
    • 1
  1. 1.Laboratory of Sciences and Techniques of Automatic control and Computer Engineering (LabSTA), National School of Engineering of SfaxUniversity of SfaxSfaxTunisia
  2. 2.LIAS-ENSIPUniversity of PoitiersPoitiersFrance

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