This paper addresses the driver-automation shared driving control for lane keeping and obstacle avoidance of automated vehicles in highway traffic. The proposed shared control framework is established from a novel cooperative trajectory planning algorithm and a fuzzy steering controller. Based on polynomial functions, the cooperative trajectory planning is formulated by judiciously exploiting the information on the maneuver decision, the conflict management, and the driver monitoring. As a result, the planned trajectory of the vehicle is continuously adapted according to the driver's actions and intentions. By means of Lyapunov stability arguments, sufficient conditions in terms of linear matrix inequalities are given to design a Takagi-Sugeno fuzzy model-based controller. This robust steering controller provides a necessary assistive torque to track the planned vehicle trajectory. The new shared driving control framework allows reducing effectively the driver-automation conflict issue while offering the driver more freedom to swerve within a predefined lane. The advantages of the proposed approach are evaluated using both objective and subjective results, experimentally obtained from several human drivers and an advanced interactive dynamic driving simulator.