SYNTHESIS OF FRACTIONAL ORDER FUZZY OBSERVER FOR A FRACTIONAL ORDER TAKAGI-SUGENO MODEL WITH UNMEASURABLE PREMISE VARIABLES

Abstract

In this article, we present a novel approach: a fractional-order fuzzy observer, an extension of the Thau-Luenberger observer, specifically designed for nonlinear systems characterized by commensurate non-integer order Takagi-Sugeno models. This work makes significant contributions in two key areas. Firstly, both the activation functions of the model and the Lipschitz fractional-order fuzzy observer are dependent on unmeasurable variables, particularly the system's state. Secondly, our proposed fuzzy observer explicitly incorporates the system's initial conditions. The stability conditions of the fractional-order fuzzy observer are expressed through Bilinear Matrix Inequalities, which are then converted into linear matrix inequalities (LMIs). Subsequently, numerical simulations are conducted to demonstrate the efficacy of our proposed estimator.