Polynomial Fuzzy Systems: Stability and Control

  • José Luis Pitarch
  • Antonio Sala
  • Carlos Vicente Ariño
Part of the Atlantis Computational Intelligence Systems book series (ATLANTISCIS, volume 9)


This chapter extends the well-known "sector nonlinearity" Takagi-Sugeno fuzzy modelling methodology for nonlinear systems to the polynomial framework. The idea is to "embed" the nonlinearities between a convex combination of polynomial vertex models. Once such models are available, stability analysis and control design can be carried out via sum-of-squares optimization. However, the major part of existent results in literature do not pay attention to the validity region of the obtained solution. This chapter addresses such problems in a polynomial framework and presents a methodology in order to estimate the domain of attraction, which improves over classical literature results.



Research in this area is supported by Spanish government: projects DPI2011-27845-C02-01, DPI2011-27845-C02-02.


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Copyright information

© Atlantis Press and the authors 2014

Authors and Affiliations

  • José Luis Pitarch
    • 1
  • Antonio Sala
    • 2
  • Carlos Vicente Ariño
    • 3
  1. 1.Systems Engineering and Control DepartmentUniversidad de ValladolidValladolidSpain
  2. 2.Systems Engineering and Control Department, I. U. de Automática e Informática Industrial (ai2)Universitat Politècnica de ValènciaValenciaSpain
  3. 3.Systems Engineering and Design DepartmentUniversitat Jaume I de CastellónCastellónSpain

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