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 fuzzy-model-based (FMB) control systems. Similar to many previous approaches, stability conditions are represented in the form of multi-dimensional fuzzy summation. To investigate the system stability, the inequalities of p-dimensional fuzzy summation are expanded to n-dimensional fuzzy summation (n >= p). Then the boundary and regional information of membership functions are utilized for relaxation of stability analysis results. In the first step 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. This approach is named Global-Membership-Function-Shape-Dependent (GMFSD). The second approach is named Regional-Membership-Function-Shape-Dependent (RMFSD) of which the operating region is partitioned to sub-regions and the boundary information of membership functions on each operating sub-region is employed to facilitate the stability analysis for further relaxation of stability conditions. Numerical example is given to demonstrate the effectiveness of the proposed stability conditions.