Maximum Allowable Loss Probability for Consensus of Multi-Agent Systems Over Random Weighted Lossy Networks

This note studies the consensus seeking problem for a team of general linear dynamical agents that communicate via a weighted random lossy network. Linear state feedback consensus protocols are applied and both the weights and feedback gain are treated as control parameters in the protocol. It is shown that the weights and the link loss probabilities of a network have non-negligible effects on the consensus seeking ability of multi-agent systems. Firstly, a weight condition characterized by the eigenvalues of the weighted Laplacian matrix is given for systems over ideal communication networks without packet losses. Secondly, based on stochastic stability analysis a maximum allowable loss probability bound is proposed for systems over random lossy networks. As long as the link loss probabilities of the network are less than this bound and the mean topology has spanning trees, there exist linear protocols solving the mean-square consensus problem of the system.