A robust weighted gain-scheduling H $_{\mathbf {\infty }}$ control design for ground vehicles possessing steer-by-wire and drive/brake-by-wire functions is presented in this paper. The main control objective is to track vehicle yaw rate reference as well as to regulate vehicle lateral velocity with the hand-wheel steering angle and the external yaw moment as two control efforts. Two major challenges are overcome: 1) the backlash-type hysteresis embedded in the steering system introduces an additional disturbance term to the system and 2) the vehicle longitudinal velocity and the tire cornering stiffnesses are considered varying. Since the external inputs (reference) and backlash-type hysteresis are both involved in the system model, we propose to design a weighted $H_{\infty }$ gain-scheduling state-feedback controller. The feedback gains can be derived by solving a sequence of linear matrix inequalities. The relative importance of the steering system hysteresis and the reference signals can be tuned by a weighting factor. In addition, the gain-scheduling skill is employed to deal with the time-varying system parameters. Furthermore, the physical limitations of the actuators are considered by an eigenvalue placement technique. Simulation studies conducted in CarSim show that the proposed controller is capable of attenuating the effects of both steering system hysteresis and the time-varying parameters. Experimental results are also presented to demonstrate the effectiveness of this control algorithm in dealing with steering system backlash-type hysteresis when tracking yaw rate references.