Robust observer design for uncertain Takagi-Sugeno model with unmeasurable decision variables: an L2 approach

This paper deals with the problem of state estimation of nonlinear uncertain systems described by uncertain multiple model form with unmeasurable decision variables. We propose two methods to attenuate the effect of modeling uncertainties and measurement noise on the state estimation. The first method is based, under some assumptions, on the second method of Lyapunov and L₂ approach. The second method allows to reduce the conservatism of the convergence conditions issued from the assumptions of first method. The convergence conditions of the observer are presented in terms of linear matrix inequality (LMI) formulation. The validity and applicability of the proposed methods are illustrated by an academic example.