Takagi-Sugeno Fuzzy Control of the Cart-Inverted Pendulum System: Linear Matrix Inequalities Application

This paper addresses the stabilization problem of an inverted pendulum system. A Takagi-Sugeno fuzzy model by incorporating an intermediate state in terms of the angular position is developed. In order to stabilize the nonlinear inverted pendulum system, a Takagi-Sugeno fuzzy state feedback control is developed. The proposed control strategy shares the same membership functions of the proposed fuzzy model. The stabilization condition is formulated as a linear matrix inequality by utilizing a Lyapunov function, in order to provide more optimized responses based on the practical limitations proposed in the article. Finally, the benefits of our proposal are illustrated via numerical simulations.