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Design of Fuzzy Observers and Output Feedback Fuzzy Controllers for Takagi–Sugeno Discrete Systems Via the Matrices Norms Approach

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Abstract

A recently developed stability analysis for Takagi–Sugeno fuzzy systems based on the products of norms of the local matrices is used here for the design of fuzzy observers and observer-based output feedback controllers. We consider both cases of measurable and unmeasurable premise variables for which conditions of global and local convergence of the estimation error are obtained and design procedures are proposed. In the latter case, given a fuzzy model with measurable and unmeasurable premises variables, we build a reduced-order fuzzy model with measurable premise variables and parameters uncertainties. Using these results, we introduce an observer-based output feedback fuzzy controller. Based on the definition of 1-norm and the ∞-norm, we show that it is possible to design separately the TS fuzzy controller and the observer to guarantee the stability of the closed loop. In order to allow for comparison, two examples from the recent literature are solved using the proposed approaches.

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  1. Laboratoire LGEPC Constantine, Department of Electrical Engineering, Ecole Nationale Polytechnique de Constantine, Constantine, Algeria

    Meroua Hamadou & Khaled Belarbi

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  1. Meroua Hamadou
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  2. Khaled Belarbi
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Correspondence to Khaled Belarbi.

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Hamadou, M., Belarbi, K. Design of Fuzzy Observers and Output Feedback Fuzzy Controllers for Takagi–Sugeno Discrete Systems Via the Matrices Norms Approach. J Control Autom Electr Syst 34, 709–719 (2023). https://doi.org/10.1007/s40313-023-00997-4

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