Stability and Stabilization Analysis of Positive Polynomial Fuzzy Systems With Time Delay Considering Piecewise Membership Functions

This paper is concerned with the stability analysis of positive polynomial-fuzzy-model-based control systems with time delay. Each of the polynomial fuzzy model and the polynomial fuzzy controller is allowed to have its own set of premise membership functions, which can improve the design and realization flexibility. Conditions showing the positivity of the system are first obtained. Then, to deal with the difficulty resulting from the mismatched premise membership functions to the stability/stabilization analysis, approximated membership functions representing the original ones are constructed, and the information of membership functions is brought into the stability conditions. This way, the stability conditions can be relaxed, since the extra knowledge on the system is considered. Stability conditions are obtained by using the sum-of squares approach based on the Lyapunov stability theory. A simulation example is provided to verify the effectiveness of this method.