  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.
