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Convergence Tools for Consensus in Multi-Agent Systems with Switching Topologies

We present two main theorems along the lines of Lyapunov's second method that guarantee asymptotic state consensus in multi-agent systems of agents in R^m with switching interconnection topologies. The two theorems complement each other in the sense that the first one is formulated in terms of the states of the agents in the multi-agent system, whereas the second one is formulated in terms of the pairwise states for each pair of agents in the multi-agent system. In the first theorem, under the assumption that the interconnection topology is uniformly strongly connected and the agents are contained in a compact set, a strong form of attractiveness of the consensus set is assured. In the second theorem, under the weaker assumption that the interconnection topology is uniformly quasi strongly connected, the consensus set is guaranteed to be uniformly asymptotically stable.