Abstract
The controllability of networks comprising linearly coupled identical subsystems is examined from a modal perspective. The eigenvalues of the network model are classified into the following two groups based on the subsystem structure:network-invariant modes, which have very high multiplicity regardless of the network’s topology; and special-repeat modes, which have bounded multiplicity. In this article, we demonstrate that models with network-invariant modes are uncontrollable unless a sufficient fraction of the subsystems are actuated in any weakly connected partition, subject to a diagonalizability condition on the network matrix. Meanwhile, the controllability reduces to a purely graph-theoretic condition when the network model has only special-repeat modes. This characterization also differentiates the controllability of built networks with fixed interconnections from multiagent systems with designable protocols.
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