Stability analysis of the simplest Takagi–Sugeno fuzzy control system using circle criterion

In this paper, we present two sufficient conditions in the frequency domain for the global stability analysis of the simplest Takagi–Sugeno (T–S) fuzzy control system, based on the circle criterion and its graphical interpretation. These conditions are significant in graphically designing the simplest T–S fuzzy controller in the frequency domain. Four numerical examples are provided to demonstrate the efficiency of our two frequency domain-based conditions. Furthermore, this T–S fuzzy controller and the linear proportional controllers are also compared. It is concluded that the simplest T–S fuzzy controller can outperform the linear proportional controllers in a noisy environment with external disturbances.