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Improved LMI Conditions for Local Quadratic Stabilization of Constrained Takagi–Sugeno Fuzzy Systems

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Abstract

This paper is devoted to the control synthesis of constrained Takagi–Sugeno (T–S) fuzzy systems. These systems are subject to multiple constraints, namely actuator saturation, system state constraints, and also \({\mathcal {L}}_2\)-disturbances. Using descriptor redundancy approach, new design conditions guaranteeing the existence of an input-saturated parallel distributed state feedback compensator are formulated as an LMI optimization problem with extra matrix decision variables. Differently from most of results dealing with the same local control context of constrained T–S systems, a generalized sector condition is used to handle effectively the nonlinearity of the control input. The use of a descriptor redundancy representation in conjunction with a sector condition for actuator saturation allows to reduce significantly the design conservatism while keeping a simple control structure. The effectiveness of the proposed method compared to many recent works is clearly demonstrated by means of numerical examples.

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Acknowledgments

This work was supported in part by the Program “Vehicle for the Future” via ADEME (French Environment and Energy Management Agency), the European Community (through the FEDER European Funds for Regional Development), the region Hauts-de-France in the framework of the CERVIFER project; in part by the International Campus on Safety and Intermodality in Transportation, the Délégation Régionale à la Recherche et à la Technologie, the Ministère de l’Enseignement Supérieur et de la Recherche and the Centre National de la Recherche Scientifique (CNRS); and in part by the Mexican Agency PRODEP via Project No. DSA/103.5/16/10200. The authors gratefully acknowledge the support of these institutions.

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Authors and Affiliations

  1. IRCCyN - UMR CNRS 6597, École des Mines de Nantes, Nantes, France

    Anh-Tu Nguyen

  2. Department of Electrical and Electronics Engineering, Sonora Institute of Technology, Obregón, Sonora, Mexico

    Raymundo Márquez

  3. LAMIH - UMR CNRS 8201, University of Valenciennes, Famars, France

    Thierry-Marie Guerra & Antoine Dequidt

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  1. Anh-Tu Nguyen
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  2. Raymundo Márquez
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  3. Thierry-Marie Guerra
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  4. Antoine Dequidt
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Correspondence to Anh-Tu Nguyen.

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Nguyen, AT., Márquez, R., Guerra, TM. et al. Improved LMI Conditions for Local Quadratic Stabilization of Constrained Takagi–Sugeno Fuzzy Systems. Int. J. Fuzzy Syst. 19, 225–237 (2017). https://doi.org/10.1007/s40815-016-0269-7

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