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Stability of Nonlinear System Using Takagi–Sugeno Fuzzy Models and Hyper-Rectangle of LMIs

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Abstract

This paper presents a theorem based on the hyper-rectangle defined by the closed set of the time derivatives of the membership functions of Takagi–Sugeno fuzzy systems. This result is also based on Linear Matrix Inequalities and allows the reduction of the conservatism of the stability analysis in the sense of Lyapunov. The theorem generalizes previous results available in the literature.

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Acknowledgments

The authors gratefully acknowledge the partial financial support by FAPESP and CNPq from Brazil.

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Authors and Affiliations

  1. CMCG—Colégio Militar de Campo Grande, Av. Presidente Vargas, 2800 Santa Carmélia, Campo Grande, MS, 79000-810, Brazil

    Jarbas Antônio Guedes

  2. Department of Electrical Engineering, UNESP—Univ Estadual Paulista, Campus of Ilha Solteira, Av. José Carlos Rossi 1370, Ilha Solteira, SP, 15385-000, Brazil

    Marcelo Carvalho Minhoto Teixeira, Rodrigo Cardim & Edvaldo Assunção

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  1. Jarbas Antônio Guedes
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  2. Marcelo Carvalho Minhoto Teixeira
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  3. Rodrigo Cardim
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  4. Edvaldo Assunção
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Correspondence to Jarbas Antônio Guedes.

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Guedes, J.A., Teixeira, M.C.M., Cardim, R. et al. Stability of Nonlinear System Using Takagi–Sugeno Fuzzy Models and Hyper-Rectangle of LMIs. J Control Autom Electr Syst 24, 46–53 (2013). https://doi.org/10.1007/s40313-013-0015-4

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  • DOI: https://doi.org/10.1007/s40313-013-0015-4

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