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This paper proposes a control architecture for autonomous lane keeping by a vehicle. In this paper, the vehicle dynamics consist of two parts: lateral and longitudinal dynamics. Therefore, the control architecture comprises two subsequent controllers. A longitudinal model predictive control (MPC) makes the vehicle track the desired longitudinal speeds that are assumed to be generated by a speed planner. The longitudinal speeds are then passed to a lateral MPC for lane keeping. Due to the dependence of the lateral dynamics on the longitudinal speed, they are represented in a linear parameter-varying (LPV) form, where its scheduling parameter is the longitudinal speed of the vehicle. In order to deal with the imprecise information of the future longitudinal speed (the scheduling parameter), a bound of uncertainty is considered around the nominal trajectory of the future longitudinal velocities. Then, a tube-based LPV- MPC is adopted to control the lateral dynamics for attaining the lane keeping goal. In the end, the effectiveness of the proposed methods is illustrated by carrying out simulation tests.