Consensus behavior of agents in networked systems under general communication topologies

In this paper, we study consensus problems and some related topics in networked dynamic systems with single-integrator dynamics. First, by introducing two useful definitions: "leader" and "follower" with respect to consensus functions, the consensus property of systems is well characterized. For systems with general weakly connected communication topologies, we partition the agents into two groups: boundary agents and internal agents, and prove that the states of internal agents converge to a convex combination of boundary agents. Finally, we extend the same idea to the formation control of vehicles and obtain some useful results