SOS-based Stability Analysis of Polynomial Fuzzy Control Systems via Polynomial Membership Functions

This paper presents stability analysis of polynomial fuzzy control systems using Sum-Of-Squares (SOS) approach. To take continuous form of membership functions into the stability analysis, based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived where each term contains product of polynomial fuzzy model and polynomial fuzzy controller membership functions. Then each product term is approximated by polynomials in the partitioned operating domain of membership functions. Regarding to the derived conditions in all sub-regions, SOS-based stability conditions are formed. The proposed approach can be utilized for stability analysis of polynomial fuzzy control system in which fuzzy model and fuzzy controller do not share the same membership functions named non-PDC design technique. The solution of the SOS-based stability conditions can be found numerically using the SOSTOOLS which is a free third-party MATLAB Toolbox. Numerical example is given to illustrate the effectiveness of the proposed stability conditions.