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Compared with the traditional front-wheel- steering (FWS) vehicles, four-wheel-independent-steering (4WIS) vehicles have better handing stability and path-tracking performance. In view of this, a novel 4WIS electric vehicle (EV) with steer-by-wire (SBW) system is proposed in this paper. As to the 4WIS EV, a linear quadratic regulator (LQR) optimal controller is designed to make the vehicle track the target path based on the linear dynamic model. Taking the effect of uncertainties in vehicle parameters into consideration, a robust controller utilizing μ synthesis approach is designed and the controller order reduction is implemented based on Hankel-Norm approximation. In order to evaluate the performance of the designed controllers, numerical simulations of two maneuvers are carried out using the nonlinear vehicle model with 9 degrees of freedom (DOF) in MATLAB/Simulink.