Relaxed LMI-Based Stability Conditions for Takagi–Sugeno Fuzzy Control Systems Using Regional-Membership-Function-Shape-Dependent Analysis Approach

This paper presents relaxed stability conditions for Takagi-Sugeno (T-S) fuzzy-model-based control systems. It is assumed that the stability conditions are represented by some inequalities in the form of a p-dimensional fuzzy summation. To investigate the system stability, the inequalities are expanded to n-dimensional fuzzy summation (n ges p). The boundary and regional informations of membership functions are then utilized for relaxation of stability analysis results. Two analysis approaches are proposed in this paper. The first approach is called the global-membership-function-shape-dependent approach, in which the lower and upper bounds of the membership functions, and its products from 2 to n in the full operating domain, are considered in the stability analysis. The second approach is named as the regional-membership-function-shape-dependent approach in which the operating region is partitioned to subregions, and the boundary information of membership functions on each operating subregion is employed to facilitate the stability analysis. In both approaches, by the help of the boundary and/or regional information of the membership functions, some inequality constraints in the form of multidimensional fuzzy summation containing some slack matrices are constructed. Stability conditions in the form of linear matrix inequalities (LMIs) are derived. Numerical examples are given to demonstrate the effectiveness of the proposed stability conditions.