Design of polynomial controllers for a two-link robot arm using sum-of-squares approachs

This paper proposes the design of polynomial fuzzy controller for an MIMO two-link arm using sum-of-squares (SOS) approach. The polynomial fuzzy framework is utilized to represent the equation of the two-link robot arm, which is more general and effective than well-known Takagi-Sugeno (T-S) fuzzy model. The polynomial Lyapunov approach is applied to analyze and derive the stability conditions of the polynomial fuzzy system, which is more relaxed than linear matrix inequality (LMI) approach to T-S fuzzy modeling and control. According to the SOS approach, the parallel distributed compensation (PDC) controller is obtained to track the state trajectory of a reference model.