ɛ-Dependent Controllability for Two Time-Scale Systems

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 obtain ɛ-dependent controllability criteria. Examples indicate that the ɛ-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.