Rehabilitation robotics is a field of research in continuous growth and evolution. Its main purpose is to develop suitable robotics devices and control strategies to assist patient's movements during trainings. To do that, advanced control algorithms and implementation of suitable force feedback for these robotic devices have been developed for rehabilitation purposes. In particular, some of these systems are designed to assist patients in completing the desired movements, providing the minimum force necessary. Thus, a direct human-robot interaction is unavoidable. For this reason, in such cases, control stability issues and safety of the system become crucial. A non-linear adaptive impedance controller, based on position errors, which aims to achieve a desired “assist-as-needed” behaviour during the rehabilitation process, has been developed in a previous work and described in [1]. However, a no straightforward stability proof of the overall system can be obtain, due to non-linear and time-varying nature of such controller. This paper is focused on the formal stability analysis of such adaptive assistance controller. Such analysis has been carried out based on an energetic approach, taking advantages of the Lyapunov theory.