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Observer-Based Output Feedback Control Using Invariant Polyhedral Sets for Fuzzy T–S Models Under Constraints

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Abstract

We propose a systematic design method to compute an observer-based output feedback controller for fuzzy Takagi–Sugeno (T–S) systems with unmeasurable premise variables, subject to state and control constraints, based on the theory of invariant sets. Sufficient conditions are established for a polyhedron defined in the augmented state-space (state + estimation error) to be positively invariant. From these conditions, a bilinear optimization problem is formulated for the simultaneous computation of the gains of the controller and of a positively invariant polyhedron guaranteeing the satisfaction of the constraints. Numerical examples illustrate the effectiveness of the method.

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Acknowledgements

The works of Carlos E.T. Dórea and Eugênio B. Castelan were supported in part by the National Council for Scientific and Technological Development—Brazil (CNPq), grants \( \# \) 309862/2019-1 and 311567/2021-5, respectively.

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Author notes

  1. Carlos E. T. Dórea and Eugênio B. Castelan have contributed equally to this work.

Authors and Affiliations

  1. UFRN-CT-DCA, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-900, Brazil

    Isaac D. Isidório & Carlos E. T. Dórea

  2. DAS/CTC/UFSC, Universidade Federal de Santa Catarina, Florianópolis, SC, Brazil

    Eugênio B. Castelan

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  1. Isaac D. Isidório
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  2. Carlos E. T. Dórea
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Correspondence to Isaac D. Isidório.

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Isidório, I.D., Dórea, C.E.T. & Castelan, E.B. Observer-Based Output Feedback Control Using Invariant Polyhedral Sets for Fuzzy T–S Models Under Constraints. J Control Autom Electr Syst 34, 752–765 (2023). https://doi.org/10.1007/s40313-023-01011-7

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