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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.

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Authors and Affiliations

  1. Laboratory of Sciences and Techniques of Automatic control and Computer Engineering (LabSTA), National School of Engineering of Sfax, University of Sfax, Postal Box 1173, 3038, Sfax, Tunisia

    Imen Haj Brahim & Mohamed Chaabane

  2. LIAS-ENSIP, University of Poitiers, 2 rue Pierre Brousse, Bât. B25-BP 633, 86022, Poitiers, France

    Driss Mehdi

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  1. Imen Haj Brahim
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  2. Driss Mehdi
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  3. Mohamed Chaabane
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Correspondence to Imen Haj Brahim.

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Haj Brahim, I., Mehdi, D. & Chaabane, M. Robust Fault Detection for Uncertain T–S Fuzzy System with Unmeasurable Premise Variables: Descriptor Approach. Int. J. Fuzzy Syst. 20, 416–425 (2018). https://doi.org/10.1007/s40815-017-0344-8

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  • DOI: https://doi.org/10.1007/s40815-017-0344-8

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