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This paper presents some recent work on designing a nonlinear robust control system for an uncertain nonlinear system. In this research a new approach to uncertainty modeling is presented. The method uses the feedback linearization approach to linearize the nominal nonlinear dynamics of the uncertain nonlinear system and linearizes the nonlinear uncertainties at an arbitrary point using the mean value theorem. This approach gives a multi-input multi-output (MIMO) linear uncertain system model with unstructured uncertainty. A guaranteed cost controller is then designed for the linearized MIMO model which stabilizes the original uncertain nonlinear system. In order to demonstrate the procedure and effectiveness of the proposed method, it is applied to a velocity and altitude tracking control problem of an air-breathing hypersonic flight vehicle.