A method is presented for designing a full state feedback linear control law that will ensure the robust stability and performance of a given linear uncertain system. The systems under consideration are described by state equations that depend on uncertain parameters. These uncertain parameters may be time varying. Their values are constrained to lie within known compact bounding sets. The method is based on the guaranteed cost control concept of Chang and Peng (1972). The controller gains result from the solution of a Riccati equation in which the weighting matrices depend on the uncertainty bounds. Sufficient conditions for the existence of a solution arise from the standard LQG control theory.