We report on the design of a three-axis missile autopilot using multi-objective control synthesis via linear matrix inequality techniques. This autopilot design guarantees $H_2/H_{infty}$ performance criteria for a set of finite linear models. These models are linearized at different aerodynamic roll angle conditions over the flight envelope to capture uncertainties that occur in the high-angle-of-attack regime. Simulation results are presented for different aerodynamic roll angle variations and show that the performance of the controller is very satisfactory.