This paper presents a novel shared control concept for lane keeping assist (LKA) systems of intelligent vehicles. The core idea is to combine system perception with robust control so that the proposed strategy can successfully share the control authority between human drivers and the LKA system. This shared control strategy is composed of two parts, namely an operational part and a tactical part. Two local optimal-based controllers with two predefined objectives (i.e., lane keeping and conflict management) are designed in the operational part. The control supervisor in the tactical part aims to provide a decision-making signal which allows for a smooth transition between two local controllers. The control design is based on a human-in-the-loop vehicle system to improve the mutual driver-automation understanding, thus reducing or avoiding the conflict. The closed-loop stability of the whole driver-vehicle system can be rigorously guaranteed using the Lyapunov stability argument. In particular, the control design is formulated as an LMI optimization which can be easily solved with numerical solvers. The effectiveness of the proposed shared control method is clearly demonstrated through various hardware experiments with human drivers.