Hu, Yenan; Sun, Fuchun; Liu, Huaping; Wu, Hao \(\varepsilon\)-dependent controllability for two time-scale systems. (English) Zbl 1212.93022 Tsinghua Sci. Technol. 14, No. 2, 271-280 (2009). Summary: 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 Mac-Laurin expansion method and homotopy arithmetic are introduced to obtain \(\varepsilon\)-dependent controllability criteria. Examples indicate that the \(\varepsilon\)-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. MSC: 93B05 Controllability 93C70 Time-scale analysis and singular perturbations in control/observation systems Keywords:singular perturbation method; time-scale separation; slow-fast order reduction PDFBibTeX XMLCite \textit{Y. Hu} et al., Tsinghua Sci. Technol. 14, No. 2, 271--280 (2009; Zbl 1212.93022) Full Text: DOI