This paper focuses on the stability analysis and control design methods for systems which contain data-driven elements. The motivation of the work is to bridge the gap between the results of physical models and experiments that are found during vehicle tests. It is presented a data-aided model augmentation method, which improves the accuracy of the formulated system model. Due to the incorporation of data-driven state observer, the resulted augmented model is a set of discrete time linear systems in a Linear Parameter Varying (LPV) structure. It is developed a control synthesis method for the formulated system, which results in a controller with two loops. It is also provided a stability analysis method for the closed-loop system based on the parameter-memorized approach. The developed method are applied to steering control design for automated vehicles, in which problem reinforcement learning is used for achieving the state observer. This paper presents the training of the observer, the augmentation of the physical model, the results of the control design and the stability analysis through a simulation example.