Proponents of autonomous driving pursue driverless technologies, whereas others foresee a gradual transition where there will be automated driving systems that share the control of the vehicle with the driver. With such advances it becomes pertinent that the developed automated systems need to be safe. One crucial aspect of safety is to prove that the switching between the human driver and the automated system results in stable system behavior. This paper presents the hybrid control framework used for modeling switching of control authority between manual and automated driving. Also, first results of evaluating stable switching and the inclusion of parameters to address effects of driver comfort and safety are presented. The system developed in this paper consists of an automated driving system that is a combination of a cruise control system and an automated lane keeping system. The manual driving component is modeled as a preview steering controller with a neuromuscular dynamics component. A novel feature of our approach is using the concept of hybrid automata to model the different modes of driving, using the concept of average dwell time to evaluate stability, and using metric interval temporal logic to incorporate verification of different parameters that may affect the switching. We present initial, simulation based results to validate the correctness and usability of the developed framework for future developments.