Abstract: The design of robust H_∞ tracking control law of a class of uncertain time-varying delay nonlinear systems was presented. First, the T-S(Takagi-Sugeno) delay model was employed to represent an uncertain nonlinear system with time-varying delayed state. Based on the LMI(linear matrix inequality)method, the design of the fuzzy-model-based H_∞ tracking control law was given when the uncertain is gain bounded. Using Lyapunov theory, it has been proven that the proposed method could guarantee the stability of the closed-loop system and the H_∞ tracking performance. Finally, the longitude flight control system of an aerospace vehicle under a hypersonic condition is designed by the proposed method. Simulation results demonstrate the effectiveness of the method.

Key words: nonlinear uncertain delay system, T-S modeling, tracking control, LMI, aerospace craft