Consensus in the presence of communication faults

In this paper we investigate the edge disconnection problem for a discrete-time multi-agent consensus network. We first show that if the communication network is symmetric, an edge disconnection that does not affect the connectedness of the whole network does not even affect the final consensus value. On the contrary, if the communication network is not symmetric, then, in general, an edge disconnection that preserves the strong connectedness of the communication graph nonetheless may lead to a consensus value that is different from the original one. Discernibility of the faulty network from the original one is investigated both in case the states of all the agents are available and in case only the states of a subset of the agents are available. Several equivalent conditions are derived and it is proved that the necessary and sufficient conditions for discernibility and for discernibility from the observation of a subset of agents are exactly the same and can be checked on the original state matrix and on its eigenvectors.