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Reachable sets to periodic linear systems

Elena Goncharova, Alexander Ovseevich


We study reachable sets to periodic linear impulsive control systems. Our main results consist of description of the asymptotic behavior in the long run of the reachable sets and their shapes, where shape of a set stands for the set regarded up to a linear transform. The shapes of convex bodies form a compact metric space and the asymptotics of the reachable sets determine an attractor in the space of shape. Our results shed some light on the structure of the attractor.

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