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\(\varepsilon\)-dependent controllability for two time-scale systems. (English) Zbl 1212.93022

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
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