This paper presents a new cost-effective control method for automatic lane keeping task of autonomous vehicles. To that end, the road-vehicle system is transformed into a polytopic LPV form which allows to deal with a large variation range of vehicle speed. Based on a robust static output feedback scheme, this method relies exclusively on commonly available vehicle sensors for control design and real-time implementation. Moreover, the information on the road geometry is incorporated in the control law to improve the lane keeping performance of the vehicle during curve taking. In particular, aiming to reduce the design conservatism, the limitation bounds on the vehicle acceleration are judiciously exploited in the design procedure through the use of a parameter-dependent Lyapunov function. The control design is recast as an LMI-based optimization with a line search over a scalar variable which can be effectively solved with numerical solvers. The effectiveness of the proposed lane keeping control method is clearly demonstrated by using the database of a real-world test track.