Distributed consensus of linear multi-agent systems via decentralized output feedback control approach

This paper studies the distributed consensus problem of general linear multi-agent systems (MASs) based on a novel decentralized output feedback control approach. By introducing the edge state and a directed-spanning-tree-based linear transformation method, we firstly equivalently transform the consensus problem into the decentralized output feedback stabilization control problem. Then we employ the properties of distributed fixed modes in decentralized output feedback stabilization control problem to derive a necessary and sufficient condition for ensuring the asymptotic state consensus of the MAS under the linear state feedback control. We further present a gradient descent iterative algorithm to design the gain matrix in the linear feedback consensus protocol. Finally, we give a numerical example to demonstrate the effectiveness of the theoretical results.