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

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.