Stability analysis of nonlinear-function fuzzy-model-based control systems

This paper presents the stability analysis of nonlinear-function fuzzy-model-based (FMB) control systems. A fuzzy model with nonlinear function terms is proposed to represent nonlinear plants. A fuzzy controller with the nonlinear function terms is then proposed to close the feedback loop. The nonlinear function terms enhance the capability of fuzzy modelling and feedback compensation. Following the linear-matrix-inequality (LMI) based stability analysis approach for the traditional FMB control systems, it will lead to stability conditions involving the nonlinear terms for the proposed nonlinear-function FMB control systems. As a result, the stability conditions will have an infinite number of LMIs, which make it impractical to find a feasible solution numerically using convex programming techniques. A stability analysis approach is proposed to obtain effective LMI-based stability conditions for the proposed nonlinear-function FMB control systems. Simulation examples are given to illustrate the merits of the proposed fuzzy control approach.