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Fault-Tolerant Trajectory Tracking Control for Takagi–Sugeno Systems with Unmeasurable Premise Variables: Descriptor Approach

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Abstract

This paper discusses the problem of fault-tolerant tracking control (FTTC) for fuzzy nonlinear systems with unmeasurable premise variables. To simultaneously estimate the system states and the sensor faults, a fuzzy descriptor observer is developed. Then, a fault-tolerant controller to track the desired reference trajectories is synthesized. The sufficient stability conditions of the appropriate nonlinear augmented system are derived via the Lyapunov theory and the \(H_\infty \) approach. In order to obtain both the observer and the controller gains the design conditions are formulated in Linear matrix inequality terms which can be solved using a one-step design procedure. Finally, the FTTC strategy is illustrated on a two-tank system to show its effectiveness.

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Acknowledgments

We thank the ministry of higher education and scientific research of Tunisia and AECID (A/030410/10 and AP/039213/11) for funding this work.

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Authors and Affiliations

  1. National School of Engineers of Sfax, University of Sfax, Rue Soukra, BP 1173, 3038 , Sfax, Tunisia

    H. Ghorbel, M. Souissi & M. Chaabane

  2. University of Picardie Jules Vernes (UPJV), 7, Rue Moulin Neuf, Amiens, 80000, France

    A. El Hajjaji

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  1. H. Ghorbel
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  2. A. El Hajjaji
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  3. M. Souissi
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  4. M. Chaabane
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Correspondence to A. El Hajjaji.

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Ghorbel, H., El Hajjaji, A., Souissi, M. et al. Fault-Tolerant Trajectory Tracking Control for Takagi–Sugeno Systems with Unmeasurable Premise Variables: Descriptor Approach. Circuits Syst Signal Process 33, 1763–1781 (2014). https://doi.org/10.1007/s00034-013-9728-7

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  • DOI: https://doi.org/10.1007/s00034-013-9728-7

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