Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems With Mismatched Premise Membership Functions

This paper investigates the stability of polynomial-fuzzy-model-based (PFMB) control system, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. To enhance the design flexibility, the number of rules and the shape of premise membership functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model, however, which make the stability analysis more difficult and potentially lead to conservative stability analysis result. A sum-of-squares (SOS)-based stability analysis approach using the Lyapunov stability theory is proposed to investigate the stability of the PFMB control systems and synthesize the polynomial fuzzy controller. To facilitate the stability analysis and relax the stability analysis result, the property of the membership functions and the boundary information of the membership grades and premise variables are taken into account in the stability analysis and incorporated into the SOS-based stability conditions. A simulation example is given to illustrate the effectiveness of the proposed approach.