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For a large class of random matrices $A$ and vectors $b$, we show that linearsystems formed from the pair $(A,b)$ are controllable with high probability.Despite the fact that minimal controllability problems are, in general,NP-hard, we establish universality results for the minimal controllability ofrandom systems. Our proof relies on the recent developments of Nguyen-Tao-Vuconcerning gaps between eigenvalues of random matrices.

Controllability of random systems: Universality and minimal controllability