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Birth of the shape of a reachable set

Alexander Ovseevich, Elena Goncharova
We address a linear control system under geometric constraints on control and study its reachable
sets starting at zero time from the origin. The main result is the existence of a limit shape of the
reachable sets as the terminal time tends to zero. Here, a shape of a set stands for the set
regarded up to an invertible linear transformation. Both autonomous and non-autonomous cases are
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