Users of shared control systems change their behavior in the presence of assistance, which conflicts with assumpts about user behavior that some assistance methods make. In this paper, we propose an analysis technique to evaluate the user's experience with the assistive systems that bypasses required assumptions: we model the assistance as a dynamical system that can be analyzed using control theory techniques. We analyze the shared autonomy assistance algorithm and make several observations: we identify a problem with runaway goal confidence and propose a system adjustment to mitigate it, we demonstrate that the system inherently limits the possible actions available to the user, and we show that in a simplified setting, the effect of the assistance is to drive the system to the convex hull of the goals and, once there, add a layer of indirection between the user control and the system behavior. We conclude by discussing the possible uses of this analysis for the field.