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

Abstract

This chapter investigates the stability of polynomial fuzzy model-based control systems by treating the membership functions and system states as symbolic variables. The information of membership functions is considered in the stability analysis and brought to the SOS-based stability conditions. Techniques are proposed to introduce slack matrix variables carrying the information of membership functions, including the property of membership functions, boundary information of membership functions and boundary information of premise variables, to the SOS-based stability conditions without increasing much the computational demand. Details of mathematical derivation are shown to help readers follow easily the analysis. A simulation example is given to show how to apply the obtained stability conditions during the control design and demonstrate the merits of the proposed stability analysis results.