Novel membership-function-dependent stability condition for T-S fuzzy systems

This paper presents an idea to further simplify and relax the linear matrix inequality (LMI) stability conditions of Takagi-Sugeno (T-S) fuzzy systems. By considering the distribution of membership functions in a unified space, we can easily find the overall relation of the original nonlinear system and its approximated local subsystems. Based on the theory of convex combination, the upper-bounds and lower-bounds of each membership functions can be directly used to construct less conservative LMI conditions. The cases of both Type-1 and Type-2 systems are considered, and examples are provided to illustrate the achieved improvement.