Static output-feedback stabilization for time-delay Takagi-Sugeno fuzzy systems

The static output-feedback control of fuzzy models is one of the most challenging problems in the fuzzy control field. In this paper, an approach to design a static output-feedback control for discrete-time-delay fuzzy models is proposed. Based on a quadratic Lyapunov function, sufficient conditions in terms of bilinear matrix inequalities (BMIs) are derived for asymptotic stability. To design a static output-feedback stabilizing controller, sufficient conditions are formulated into a set of linear matrix inequalities using some matrix transformations, which make possible to calculate directly the desired controller. A numerical example is given to illustrate the applicability of the proposed approach.