This paper investigates the controllability of two time-scale systems using both the time-scale separation model and the slow-fast order reduction model.This work considers the effect of a singular perturbation parameter on the model transformations to improve the criterion precision.The Maclaurin expansion method and homotopy arithmetic are introduced to obtainε-dependent controllability criteria.Examples indicate that theε-dependent controllability criteria are more accurate and that the controllability of two time-scale systems does not change during model transformations with these more accurate forms.
