This paper describes the development and analysis of gain-scheduled, multi-variable H∞ control law for the conversion of a linear parameter varying (LPV) model of a High-Speed Autonomous Rotorcraft Vehicle (HARVee), an experimental tilt-wing aircraft. Tilt-wing aircraft combine the high-speed cruise capabilities of a conventional airplane with the vertical takeoff and station keeping abilities of a helicopter by rotating their wings at the fuselage. Changing between cruise and hover flight modes in mid-air is referred to as the conversion process, or simply conversion. A nonlinear aerodynamic model was previously developed that captures the unique dynamics of the tilt-wing aircraft. An H∞ design methodology was used to develop linear controllers along various operating points of a conversion trajectory. The development of these control systems was governed not only by performance specifications at each particular operating point, but also by the unique requirements of a gain-scheduled conversion control system. The performance of the resulting conversion closed-loop systems is analyzed in the frequency and time domains. Performance robustness with respect to variation in the location of the center of gravity (eg) has been studied.