Polynomial fuzzy control of an inverted pendulum system by sum-of-squares approach

This paper presents the polynomial fuzzy control of dc motor controlling an inverted pendulum via a gear train. The polynomial Lyapunov function is utilized to analyze and derive the stability conditions of the polynomial fuzzy system with decay rate, which is more relaxed than linear matrix inequality approach to T-S fuzzy modeling and control. By the polynomial fuzzy model of the inverted pendulum system, the polynomial fuzzy controller is designed via parallel distributed compensation (PDC). The derived stability conditions are represented in terms of sum-of-squares (SOS) to guarantee the closed-loop system is global stable. Computer simulations demonstrate that the polynomial fuzzy controller can reduce the convergence time and decrease the control energy.