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

Kevin Guelton (1) , Tahar Bouarar (1) , Noureddine Manamanni (1)

1 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804

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.

Mots clés: Fuzzy control; Takagi-Sugeno systems; Dynamic output feedback; Non-quadratic stabilization; Fuzzy Lyapunov function; Descriptor redundancy

Domaines: Automatique

Kevin Guelton, Tahar Bouarar, Noureddine Manamanni. Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems - A descriptor redundancy approach. Fuzzy Sets and Systems, 2009, 160 (19), pp.2796-2811. ⟨10.1016/j.fss.2009.02.008⟩. ⟨hal-00793238⟩