On observer design for nonlinear Takagi-Sugeno systems with unmeasurable premise variable

Dalil Ichalal (1) , Benoît Marx (2) , Didier Maquin (2) , José Ragot (2)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 CRAN - Centre de Recherche en Automatique de Nancy

In this paper, we propose a method for state estimation of nonlinear systems represented by Takagi- Sugeno (T-S) models with unmeasurable premise variables. The main result is established using the differential mean value theorem which provides a T-S representation of the differential equation generating the state estimation error. This allows to extend some results obtained in the case of measurable premise variables to the unmeasurable one. Using the Lyapunov theory, stability conditions are obtained and expressed in term of linear matrix inequalities. Furthermore, an extension for observer design with disturbance attenuation performance is proposed. Finally, this approach is illustrated on a DC series motor and compared to the existing approaches.

Keywords: Takagi-Sugeno systems; state estimation; differential mean value theorem; Lyapunov stability analysis; linear matrix inequality

Domains: Engineering Sciences [physics]; Automatic

Dalil Ichalal, Benoît Marx, Didier Maquin, José Ragot. On observer design for nonlinear Takagi-Sugeno systems with unmeasurable premise variable. 4th International Symposium on Advanced Control of Industrial Processes, Adconip 2011, May 2011, Hangzhou, China. pp.353--358. ⟨hal-00545702⟩