Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems Using Switching Polynomial Lyapunov Function

This paper investigates the stability problem of polynomial-fuzzy-model-based control system, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. A switching polynomial Lyapunov function consisting of a number of local polynomial Lyapunov functions is proposed to investigate the system stability. It demonstrates a nice property in favor of the stability analysis that each local polynomial Lyapunov function transits continuously to each other. As different local polynomial Lyapunov functions are employed to investigate the system stability according to the operating domain, relaxed stability conditions compared with the stability analysis result with a common Lyapunov function can be developed. In order to allow a greater design flexibility for the polynomial fuzzy controller, the proposed polynomial-fuzzy-model-based control scheme does not require that both the polynomial fuzzy model and polynomial fuzzy controller share the same premise membership functions. Stability conditions in terms of sum of squares are obtained to guarantee system stability and facilitate control synthesis. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed polynomial fuzzy control scheme.