Stability analysis for a class of Takagi–Sugeno fuzzy control systems with PID controllers

A new stability analysis method for a class of fuzzy control systems based on Takagi–Sugeno models and PID controllers is proposed in this paper. It has shown that the traditional Takagi–Sugeno fuzzy state models with certain matrix structures are equivalent to fuzzy transfer function models, which have two consequents in each rule. Then, when the PID controllers utilising the overall closed-loop system behave like an uncertain affine system. So we can use some results from robust control theory to analyse the system stability.