The Stabilization Condition of Continuous Affine Fuzzy Systems Under Imperfect Premise Matching

In this paper, the stabilization condition for the continuous time affine fuzzy system is proposed under the imperfect premise matching. The affine fuzzy system means that the Takagi-Sugeno (T-S) fuzzy system contains the constant bias terms unlike the homogeneous fuzzy system. The constant bias terms make difficult to analyze the characteristics of the affine fuzzy system. In order to solve this problem, this paper employs the specific transformation matrix related to the input matrix. Furthermore, the concept of the imperfect premise matching is considered to reduce the implementation cost caused by complicated membership functions. In other words, the affine fuzzy controller which does not share the membership functions of system is designed to obtain the stabilization condition of the affine fuzzy systems. Finally, the effectiveness of proposed approach is verified with a numerical example.