This brief presents a new method of analyzing stability and design of a controller for an electric power steering (EPS) system. The most important task when designing a steering system is ensuring that the driver is pleased with how the steering feels. The way that the steering feels is dependent upon the assist torque map. The assist torque map is a one-to-one map between sensed driver torque and assist motor torque that varies with the cars speed. However, an assist torque map cannot be applied alone as an EPS controller because of high level of steering assist gain and nonlinearity of the torque map. Both elements of torque map can result in instability, which leads to vibration or divergence of the steering system. Therefore, an EPS system always needs to be designed with a stabilizing compensator and an assist torque map. The objective of designing a compensator is to stabilize the system with robustness and attenuate any unpleasant vibration. This brief presents a mechanical model of the EPS system and demonstrates a method to identify the model parameter. Based on the EPS model, stability of the system with an approximate linear torque map and nonlinear torque map is analyzed. Furthermore, criteria for designing the stabilizing compensator are suggested. Leadlag compensators with different parameters are applied with the torque map in simulations, and vehicle experiments are performed to verify the theoretical analysis.