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Work presented in this book introduce new approaches to designing robust nonlinear controllers for a class of nonlinear uncertain systems. It integrates the conventional feedback linearization method with the robust control schemes such as minimax LQR and minimax LQG controllers in a systematic way. The main objective of this research is to apply the proposed method to the case of an air-breathing hypersonic flight vehicle (AHFV) control problem. In this work, we consider both rigid and flexible nonlinear models of a hypersonic flight vehicle and synthesized velocity and altitude nonlinear tracking controllers by using minimax LQR and minimax LQG controllers. The main reason to use minimax control theory is that it gives a systematic way to design a robust controller and also allows for time varying uncertainty.