Kalman rank condition is necessary and sufficient for arbitrarily fast steering of invertible rearrangements of identical linear systems, but no continuous universal feedback law exists.
Control on the manifolds of mappings with a view to the deep learning
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Collective steering in finite time: controllability on $\text{GL}^+(n,\mathbb{R})$
Kalman rank condition is necessary and sufficient for arbitrarily fast steering of invertible rearrangements of identical linear systems, but no continuous universal feedback law exists.