This paper addresses the problem of designing control systems for steering an autonomous vehicle, for varying speed, ensuring stability and sustaining performance, taking into account comfort and safety. A novel automatic lateral control architecture is proposed combining Linear Parameter Varying (LPV) control theory and the Pure-Pursuit algorithm. The response of the robust controller is investigated for tracking a reference trajectory. The implementation is based on the reduction of the polytopic LPV model. In addition, to illustrate the results, the synthesized controller has been tested first in simulations, and then to an automated electric Renault Zoe in a test track providing encouraging results.