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.
Products of positive definite matrices
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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.