@article{HU2009, 
author = {Yenan HU and Fuchun SUN and Huaping LIU and Hao WU},
title = {ε-Dependent Controllability for Two Time-Scale Systems},
year = {2009},
journal = {Tsinghua Science and Technology},
volume = {14},
number = {2},
pages = {271-280},
keywords = {controllability, singular perturbation method, time-scale separation, slow-fast order reduction, Maclaurin expansion, homotopy arithmetic},
url = {https://www.sciopen.com/article/10.1016/S1007-0214(09)70040-9},
doi = {10.1016/S1007-0214(09)70040-9},
abstract = {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 ε-dependent controllability criteria. Examples indicate that the ε-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.}
}