A new design method of H∞ state feedback gain-scheduling controller for T-S fuzzy systems

In this article, a new systematic synthesis method is proposed to design a full state feedback gain-scheduling controller for Takagi-Sugeno (T-S) fuzzy plants. Both the stability and H∞ performance of the closed-loop system are considered. More specifically, by using the information that the degree of membership function is constrained within the interval [0, 1], the T-S fuzzy plant is transformed into the form of linear fractional transformation (LFT). Within the framework of LFT, the problem of stability and H∞ performance for the T-S fuzzy system can be reformulated into a convex optimization problem which can be approached by solving a set of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness of the proposed method.