Asymptotic stability analysis of TSK fuzzy PI control system using circle criterion

In this paper, we study asymptotic stability of the Takagi-Sugeno-Kang (TSK) fuzzy PI control system using the circle criterion theorem. We first divide a TSK fuzzy PI controller into a memoryless nonlinear part and a linear dynamic unit, and merge the linear dynamic unit with a linear plant to be controlled and form a new augmented plant. The system is then reconstructed as a new interconnected form of the augmented linear plant and the memoryless nonlinear part. We then derive transfer function matrix of the augmented linear plant and sector condition of the memoryless nonlinear part. Based on the derived transfer function matrix and the sector condition, we determine sufficient conditions that guarantee asymptotic stability of the TSK fuzzy PI control system by using the circle criterion. Two examples are presented to demonstrate the feasibility of the proposed method.