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This report presents a multivariable controller design for a generic missile travelling at hypersonic speed. The controller is based on the theory of optimal control, and the solution is provided by a feedback controller known as a Linear Quadratic Regulator (LQR) for tracking the demands (lateral acceleration and roll rate) as closely as possible while keeping the actuator efforts (for deflecting aileron, elevator and rudder) small. In the computer simulation, the missile model is subject to various hypersonic flight conditions and gain scheduling is exercised as a function of dynamic pressure. The intial study assumes perfect knowledge of all the states for the controller design. Subsequently, a state observer (kalman filter) is introduced into the design to reflect a more practical synthesis where some of the states need to be estimated