Opinion Dynamics with Persistent Leaders

This paper revisits the problem of agreement seeking in a social network under the influence of leaders. The persistence of the leader's effect on the opinions of other agents is characterized by the total weight that they place on the leader's information over time. If this weight is infinite, then the leader is called persistent. Our results describe the asymptotic behavior of network opinions towards the state of a persistent leader in both cases of networks with fixed and switching topologies. We also show that only persistent leaders are able to drive the network to the leader's constant state.