Consensusability of discrete-time multi-agent systems under state feedback control

This paper investigates the problem when discrete-time multi-agent dynamic systems are consensusable, and how to synthesize the distributed consensus feedback control law when the consensusability holds. We focus on multi-agent systems over the undirected graph of the communication topology and derive the consensusability condition. Our results are constructive and provide an explicit synthesis procedure for designing the distributed feedback control protocols based on local information that enable all agents to reach the prescribed consensus asymptotically. The consensusability is related to the gain margin problem under state feedback and output injection that is also solved in this paper.