A fuzzy sliding mode observer for the nonlinear uncertain system based on T-S model

This paper addressed the analysis and design of a sliding mode observer for a class of uncertain nonlinear systems. We continue to work in [1] that proposed an approach to design the sliding mode control of same system using the control law obtained to analyze our sliding mode observer. The main idea of the paper is the development of a robust observer with respect to the uncertainties parametric type norm bounded as well as the synthesis of sufficient stability conditions of this observer. The stabilization of the observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of linear matrix inequalities (LMI). A numerical application of inverted pendulum is given to validate the theoretical results of our approach.