Polynomial Fuzzy-Model-Based Control Systems: Stability Analysis via Approximated Membership Functions Considering Sector Nonlinearity of Control Input

This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control systems, in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. In order to address the input nonlinearity, the control signal is considered to be bounded by a sector with nonlinear bounds. These nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account. With the consideration of imperfectly matched membership functions and input nonlinearity, the applicability of the PFMB control scheme can be further enhanced. To facilitate the stability analysis, a general form of approximated membership functions representing the original ones is introduced. As a result, approximated membership functions can be brought into the stability analysis leading to relaxed stability conditions. The sum-of-squares approach is employed to obtain the stability conditions based on Lyapunov stability theory. Simulation examples are presented to demonstrate the feasibility of the proposed method.