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Driver assistance systems and vehicle safety systems are meant to improve the driving performance of a driver. Despite increased efforts in educating public at large on the danger of impaired driving in recent years, the problem is not alleviated and drunk driving is still one of the major causes of fatal accidents. Although different models of sober drivers are available in literature, mathematical modeling of humans under the influence of alcohol / drugs in steering control of a vehicle is open. Using system identification techniques, four different linear models for these drivers are presented here. The parameters and characteristics of these models are compared with the respective models for sober drivers. Larger delay (reaction time), reduced ability of maintaining the car in the center of lane, and aggressive driving style are some of the important features of intoxicated drivers identified here. The proposed models are validated using the data collected from 50 minute driving sessions for both sober and drunk drivers. The parametric uncertainties of the model parameters are also shown.