Membership-Function-Dependent Stability Analysis of Interval Type-2 Polynomial Fuzzy-Model-Base Control Systems

In this paper, the stability analysis for interval type-2 (IT2) polynomial fuzzy-model-based (PFMB) control system using the information of membership functions is investigated. To tackle uncertainties, IT2 membership functions are used in the IT2 polynomial fuzzy model and IT2 polynomial fuzzy controller. The stability of IT2 PFMB control system is investigated based on the Lyapunov stability theory and both sets of membership function independent (MFI) and membership function dependent (MFD) stability conditions are derived on the basis of the sum-of-squares (SOS) approach. To make the stability conditions MFD, the boundary information of IT2 membership functions is used in the stability analysis. To extract richer information of IT2 membership functions, the operating domain is partitioned into sub-domains. In each sub-domain, the boundary information of IT2 membership functions and those of the upper and lower membership function are obtained. Furthermore, to further relax the conservativeness, a switching polynomial fuzzy controller, together with the informations obtained in each sub-domain, is employed in investigating the stability analysis. Numerical examples and simulation results are given to demonstrate the validity of MFD and MFD switching methods.