We study, in the spirit of [1], reachable sets for singularly perturbed linear control systems. The fast component of the phase vector is assumed to be governed by a strictly stable linear system. It is shown in loc.cit. that the reachable sets converge as the small parameter ε tends to 0, and the rate of convergence is O(ε~α), where 0 < α < 1 is arbitrary. In fact, the said rate of convergence is ε log 1/ε. Under an extra smoothness assumption we find the coefficient of ε log 1/εin the asymptotics of the support function of the reachable set.
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