Stability Analysis of Polynomial Fuzzy Model-Based Control Systems with Mismatched Premise Membership Functions Through Taylor Series Membership Functions

Abstract

This chapter investigates the stability of polynomial fuzzy model-based control systems by bringing the approximated membership functions into the SOS-based stability conditions. Various approximation methods of membership functions are reviewed and their characteristics are discussed. Using the Taylor series expansion, the original membership functions are represented by approximated membership functions which are a weighted sum of local polynomials in a favorable form for stability analysis. SOS-based stability conditions are obtained which guarantee the system stability if the fuzzy model-based control system is stable at all chosen Taylor series expansion points. A simulation example is presented to illustrate the influence of the density of expansion points to the capability of stability conditions finding a feasible solution and demonstrate the effectiveness of the proposed stability conditions over some published results.