This article presents the design and validation of a fault-tolerant Y* flight controller for the Japanese Aerospace Exploration Agency's (JAXA) Multi-Purpose Aviation Laboratory- $\alpha$ (MuPAL- $\alpha$) aircraft. A structured $\mathbf{H}_{\infty}$ controller is synthesized by using non-smooth optimization to address performance and robustness constraints (specifically, uncertain actuator delays and varying airspeed) as well as loss-of-efficiency faults of a specific range with reduced online numerical complexity. The performance of the closed-loop system is validated through hardware-in-the-Ioop (HIL) simulations using the actual MuPAL- $\alpha$ aircraft, and they show that an improved fault tolerant capability is achieved when compared to Y* design robust only against the actuator delays.