Consensus problems in discrete-time multiagent systems with fixed topology

In this paper, we study the consensus problems in discrete-time multiagent systems with fixed topology. A necessary and sufficient condition for a system that solves a consensus problem is established, and the structure of consensus functions is characterized. Based on them, we introduce the standard topologies (graphs) of information flow, with which the systems can be viewed as single-leader–multi-follower systems. Moreover, the convex combination of these topologies can create a system that solves any predeterminate consensus problem. Additionally, we characterize the structural decomposition—the leaders–followers decomposition of a multiagent system, and establish a necessary and sufficient condition for an agent to be a leader.