To deal with the stability and stabilization problem of model parameter variation and the large-span maneuver flight of hypersonic vehicles, a robust stabilization control method was presented using switched polytopic systems. The dynamic variables of vehicle envelope were firstly divided into switched polytopic systems, and then the stability analysis was proved by employing switching parameter-dependent Lyapunov functions and the average dwell time method. Finally, the control synthesis was deduced for asymptotical stability of the aircraft dynamics within the envelope. Simulation results demonstrate that the control scheme qualifies satisfactory response and provides satisfactory command tracking, and the proposed method avoids the state jumping in traditional switching controllers and it is with low analysis and design conservation.