Abstract
The main purpose of the paper is to study the asymptotic behavior of reachable sets to linear time-invariant control systems with a bounded control. The issue is analyzed within a framework of shapes of reachable sets. Main results consist in an existence proof, and a rather explicit description of limit shapes of the studied reachable sets as time goes to infinity. We also state a conjecture on the structure of the set of limit shapes in the general non-autonomous case.
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