How the brain responds to non-invasive brain stimulation, such as transcranial magnetic stimulation (TMS), depends on the physiological state. In recent years, we have come to understand what happens at the stimulation site, but the whole-brain response remains unclear. Here, we consider the brain as an autonomous control system and stimuli as control inputs, and use the framework of control theory to describe the whole-brain response to brain stimuli. Our method, based on the so-called controllability gramian, can reveal not only the average controllability, i.e. how easily the brain dynamics can be "controlled" (represented as the eigenvalues of the gramian), but also in which direction the brain dynamics can be easily controlled (represented as the eigenvectors of the gramian). As a proof of concept, we applied our method to TMS-induced electroencephalographic (EEG) responses during four motor-related states and two resting states. We found that although the EEG response tends to have a greater controllable magnitude during rest than during motor-related states, the task condition cannot be distinguished from the single-shot, single-trial measurement signals. On the other hand, the controllable direction clearly distinguishes two resting states and one motor-related state from the others. These results demonstrate that EEG responses to brain stimulation can be quantitatively compared across states using controllability-based functional brain data analysis. The proposed method is expected to be used in brain stimulation application scenarios, such as elucidating individual differences in response and exploring conditions under which brain stimulation is highly effective.