In this paper, a dynamic antiwindup compensator design is proposed which augments the main controller and guarantees robust performance in the event of input saturation. This is a two stage process in which first a robust optimal controller is designed for an uncertain linear system which guarantees the internal stability of the closed loop system and provides robust performance in the absence of input saturation. Then a minimax linear quadratic Gaussian (LQG) compensator is designed to guarantee the performance in certain domain of attraction, in the presence of input saturation. This antiwindup augmentation only comes into action when plant is subject to input saturation. In order to illustrate the effectiveness of this approach, the proposed method is applied to a tracking control problem for an air-breathing hypersonic flight vehicle (AHFV).