This paper proposes a new $H_{infty}$ yaw moment control scheme using brake torque switching for improving vehicle performance and stability especially in high speed driving. In the scheme, one wheel is selected, depending on the vehicle states, at which a brake torque for control is applied. Steering angles are modeled as a disturbance to the system and the $H_{infty}$ controller is designed to minimize the difference between the performance of the vehicle and that of the desired model. Its performance robustness as well as stability robustness to system parameter variations is assured through ${mu}$-analysis. Various simulations with a nonlinear 8-DOF vehicle model show that proposed controller enhances the vehicle performance and stability under disturbances and parameter variations as well as under the normal driving condition.