Model reference tracking control design of T-S fuzzy systems with polynomial input functions

This paper proposes a fuzzy tracking control design for Takagi-Sugeno (T-S) fuzzy systems. T-S fuzzy model is used to represent the nonlinear systems subject to external disturbance. Based on Lyapunov´s direct method, the model reference tracking control scheme based on the augmented system is proposed and a nonlinear control law is derived with robust H^∞ performance. Sufficient condition is derived in terms of a state-dependent nonlinear matrix inequality and then it is converted into a sum-of-squares (SOS) optimization problem. Semi-definite programming and SOS decomposition techniques are employed to solve the optimization problem. Simulation example is given to illustrate tracking performance of the proposed method.