Topology-induced containment for general linear systems on weakly connected digraphs

The paper deals with topology-induced containment output feedback for ensuring multi-consensus of homogeneous linear systems evolving over a weakly connected communication digraph. Starting from the extension of a recent characterization of multi-consensus, a decentralized static feedback enforcing multi-consensus is designed based on a suitable network-induced decomposition; a neighborhood state-observer is proposed for completing the design. The results are finally illustrated over a simple simulated example.