Positive controllability of networks under relative actuation

Abstract

For arrays of identical linear systems coupled through relative actuation four problems are studied: controllability, positive controllability, pairwise controllability, and positive pairwise controllability. To this end, related to the eigenvalues of the system matrix, certain graphs with possibly vector-valued edge weights are constructed. It is shown that array controllability and graph connectivity are equivalent. Similar equivalences are established also between positive controllability and strong connectivity, pairwise controllability and pairwise connectivity, and positive pairwise controllability and strong pairwise connectivity.