Sum-of-squares-based stability analysis of polynomial fuzzy-model-based control systems

This paper presents the stability analysis of polynomial fuzzy-model-based control systems, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Based on the Lyapunov stability theory, the stability analysis is generalized by bringing the membership functions as polynomial variables to the stability analysis for relaxation of SOS-based stability conditions. For further relaxation of the stability analysis result, the information of membership function boundary and operating domain information is considered. It can be shown that the existing SOS and linear-matrix-inequality (LMI)-based stability conditions are a particular case of the proposed SOS-based stability conditions. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.