Erratum to "Edge Selections in Bilinear Dynamic Networks"

Arthur Castello B. de Oliveira, Milad Siami, Eduardo D. Sontag

Abstract: Lemma 2 of “Edge Selections in Bilinear Dynamical Networks” (Oliveira et al., 2024) allows one to efficiently compute a lower bound for the optimal $\mathcal {H}_{2}$-norm of a bilinear dynamical network following optimal edge selection, by showing convexity of a relaxed version of the problem. However, the proof presented is wrong in general, leaving the statement unproven. In this note, we discuss a case in which the presented result is guaranteed to hold and update our experimental results in light of this fact. Despite this problem with an auxiliary result in the article, notice that the main result in Theorem 1 remains correct, proving supermodularity of the $\mathcal {H}_{2}$-norm under edge addition.