This research develops a robust control approach for hypersonic vehicles (HV) using modern H-infinity techniques. Focusing initially on subsonic conditions, a non-linear GHAME HV model was created in MATLAB and Simulink, incorporating parametric uncertainty in aerodynamic coefficients. Linear short-period longitudinal dynamics were extracted at multiple operating points. A fixed-structure controller was synthesized using multi-objective H-infinity mixed-sensitivity techniques, addressing pitch moment coefficient uncertainty. The design was extended to account for variations in Mach number, altitude, and fuel mass. The control system was checked for robustness requirements and tested on the non-linear model.