Structural controllability and matrix nets†

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Abstract
We establish structural controllability results for matrix pairs [A, B] where A = A 0 + Σ μ iAi , B = B 0 + σ μ i, Bi , with the Ai , Bi , fixed, and the μ i , free scalar parameters. The results characterize structural controllability in several ways, via tests involving the checking of the rank or the evaluation of the determinant of various constant matrices formed from the Ai , Bi . A number of the results used as intermediate results tests for a full rank property of matrix nets, i.e. tests that check if M = M0+ ΣμiMi prescribed, μ i variable, has full rank for almost all μ i .

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