We discuss a new control method for path following of autonomous ground vehicles. First, the nonlinear vehicle system is transformed into a polytopic LPV model allowing to handle a large variation range of vehicle speed with a reasonable numerical complexity. Second, based on an LPV static output feedback scheme, the proposed controller can achieve the path following performance without requiring the costly optical sensor used to measure in real-time the sideslip angle. Third, the steering saturation is explicitly taken into account in the design procedure to improve the safety and confort of passengers. The new LPV static output feedback design is reformulated as an optimization problem under LMI constraints with a line search over a parameter. The interests of the proposed method are emphasized by numerical simulations with a nonlinear vehicle model under various driving scenarios.