Stability Analysis of Positive Polynomial Fuzzy-Model-Based Control Systems With Time Delay Under Imperfect Premise Matching

This paper deals with the stability and positivity analysis of polynomial-fuzzy-model-based (PFMB) control systems with time delay, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop, under imperfect premise matching. To improve the design and realization flexibility, the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. A sum-of-squares-based stability analysis approach using the Lyapunov stability theory is employed to investigate the positivity and stability of the PFMB control systems and synthesize the polynomial fuzzy controller. In order to relax the stability results, we propose two methods: first, membership functions are considered as symbolic variables in the stability analysis; and second, the property of the membership functions and the boundary information of the membership functions are considered in the stability analysis. A simulation example is given to illustrate the effectiveness of the proposed approach.