Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

This paper deals with the static output feedback stabilization of positive polynomial fuzzy-model-based control systems. The positive polynomial fuzzy model does not need to share the same premise membership functions with the static output feedback polynomial fuzzy controller. Unlike the state feedback control case, the static output feedback control usually leads to nonconvex stability conditions. To circumvent the problem, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a nonsingular transformation matrix. Initially, the conditions guaranteeing the resultant closed-loop systems to be positive and asymptotically stable are obtained. Moreover, the divisional approximated membership functions that carry the local information of the membership functions are employed to facilitate the stability analysis and controller synthesis. The relaxed stability conditions in terms of sum of squares are obtained based on Lyapunov stability theory. Finally, a simulation example is given to testify the validity of the analysis result.