Design of observers for Takagi-Sugeno discrete-time systems with immeasurable premise variables

Dalil Ichalal (1) , Benoît Marx (1) , José Ragot (1) , Didier Maquin (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

This paper deals with the problem of the state estimation of discrete time nonlinear systems described by Takagi-Sugeno structure with unmeasurable premise variables. The proposed observer design method is based on the use of the second method of Lyapunov and a quadratic function. Based on this procedure two methods are proposed. The convergence conditions of the observer are expressed in terms of Linear Matrix Inequalities (LMI). Finally, these two methods are compared with regard to their domains of validity.

Keywords: Multiple model approach; nonlinear observer; unknown premise variables; nonlinear discrete system; L2 optimization; linear matrix inequality

Domains: Automatic

Dalil Ichalal, Benoît Marx, José Ragot, Didier Maquin. Design of observers for Takagi-Sugeno discrete-time systems with immeasurable premise variables. 5th Workshop on Advanced Control and Diagnosis, ACD 2007, Nov 2007, Grenoble, France. pp.CDROM. ⟨hal-00188464⟩