Stabilization of Interval Type-2 Polynomial-Fuzzy-Model-Based Control Systems

In this paper, the stability of polynomial-fuzzy-model-based (PFMB) systems equipped with mismatched interval type-2 (IT2) membership functions is investigated. Unlike the membership-function-independent methods, the information and properties of IT2 membership functions are considered in the stability analysis and contained in the stability conditions in terms of sum-of-squares (SOS) based on the Lyapunov stability theory. Three methods, demonstrating their own advantages, are proposed to conduct the stability analysis for the IT2 PFMB control systems. In the first one, we divide the operating domain into subdomains and then conduct the stability analysis incorporating the information and properties of the IT2 membership functions in subdomains. Through this approach, the stability conditions can be further relaxed compared with the membership-function-independent analysis. Polynomial functions are adopted in the second method to approximate the IT2 membership functions. The advantage of this method compared with the first one is that richer information of IT2 membership functions is considered without increasing the number of SOS conditions. In the third one, we combine the advantages of both the first and the second method offering a new approach which utilizes the information and properties of the lower and upper IT2 membership functions in subdomains through simpler polynomial approximation functions. It can be shown that more relaxed stability conditions can be obtained compared with the first two methods. Numerical examples and simulations are presented to verify the effectiveness of the proposed methods.