Relaxed Stabilization Criterion for T–S Fuzzy Systems by Minimum-Type Piecewise-Lyapunov-Function-Based Switching Fuzzy Controller

This paper proposes the minimum-type piecewise-Lyapunov-function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie et al. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov functions as the Lyapunov function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov function as the Lyapunov function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.