Non-quadratic local stabilization for continuous-time Takagi-Sugeno models

Thierry-Marie Guerra (1) , Miguel Bernal (1) , Kevin Guelton (2) , Salim Labiod (3)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
2 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804
3 UMSBJ - Université Mohammed Seddik Benyahia [Jijel] | University of Jijel

This paper is concerned with non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models. The well-known problem of handling time-derivatives of membership functions (MFs) as to obtain conditions in the form of linear matrix inequalities (LMIs) is overcome by reducing global goals to the estimation of a region of attraction. Instead of parallel distributed compensation (PDC), a non-PDC control law is proposed according to the non-quadratic nature of the Lyapunov function. Examples are provided to show the advantages over the quadratic and some non-quadratic approaches.

Mots clés: Linear matrix inequalities; Non-quadratic Lyapunov function; Stabilization; Takagi-Sugeno models

Domaines: Automatique

Thierry-Marie Guerra, Miguel Bernal, Kevin Guelton, Salim Labiod. Non-quadratic local stabilization for continuous-time Takagi-Sugeno models. Fuzzy Sets and Systems, 2012, 201, pp.40-54. ⟨10.1016/j.fss.2011.12.003⟩. ⟨hal-00793244⟩