A new computational approach to stability analysis and synthesis of linguistic fuzzy control system

In this paper, stability analysis and synthesis of the type-II (Singleton-type) linguistic fuzzy control system are addressed. First, stability theorems are given for both continuous-time case and discrete-time case and they are recast in the formulation of bilinear matrix inequalities (BMIs). Continuous and discrete iterative linear matrix inequality methods are presented to obtain the feasible solution for the stability conditions represented as the BMI. The interesting feature of this paper is that the suggested method can be applied not only to the stability analysis but also to the controller synthesis. When it is applied to the synthesis of the type-II fuzzy logic controller, the resulting one can theoretically guarantee the stability of the closed-loop system. Finally, the effectiveness of the suggested method is illustrated via computer simulation.