Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi--Sugeno systems---A descriptor redundancy approach

  • Authors:

  • Kevin Guelton;Tahar Bouarar;Noureddine Manamanni

  • Affiliations:

  • CReSTIC, EA3804, URCA, Université de Reims Champagne-Ardenne, Moulin de la House BP1039, 51687 Reims Cedex 2, France;CReSTIC, EA3804, URCA, Université de Reims Champagne-Ardenne, Moulin de la House BP1039, 51687 Reims Cedex 2, France;CReSTIC, EA3804, URCA, Université de Reims Champagne-Ardenne, Moulin de la House BP1039, 51687 Reims Cedex 2, France

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2009

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Abstract

This paper deals with Takagi-Sugeno (T-S) systems stabilization based on dynamic output feedback compensators (DOFC). In fact, only few results consider DOFC for T-S systems and most of them propose quadratic Lyapunov functions to provide stability conditions, which may lead to conservatism. In this work, to overcome this drawback and to enhance the closed-loop transient response, we provide for T-S uncertain closed-loop systems non-quadratic stability conditions. Based on a fuzzy Lyapunov candidate function and the descriptor redundancy property, these stability conditions are written in terms of linear matrix inequalities (LMI). Afterward, the DOFC is designed with H"~ criterion in order to minimize the influence of external disturbances. Finally, a few academic examples illustrate the efficiency of the proposed approaches.