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Resilient Continuous-Time Consensus in Fractional Robust Networks

In this paper, we study the continuous-time consensus problem in the presence of adversaries. The networked multi-agent system is modeled as a switched system, where the normal agents have integrator dynamics and the switching signal determines the topology of the network. We consider several models of omniscient adversaries under the assumption that at most a fraction of any normal agent's neighbors may be adversaries. Under this fractional assumption on the interaction between normal and adversary agents, we show that a novel graph theoretic metric, called fractional robustness, is useful for analyzing the network topologies under which the normal agents achieve consensus.