The one-dimensional theory of how an ignited tokamak can be controlled by a vertical field is equivalent to the zero-dimensional theory (in the sense that the stability is described by the same ω) with respect to all perturbations (local or global) which move the system outside the marginal ignition point. This result holds on the assumption (verified in a particular example) that the effect of those particular perturbations which produce an energy unbalance locally, while the system globally remains at marginal ignition, can be ignored.