  Classic models on opinion dynamics usually focus on a group of agents forming
their opinions interactively over single issue. Yet generally consensus can not
be achieved over single issue when agents are not completely open to
interpersonal influence. In this paper, opinion consensus in social networks
with stubborn agents is considered over issue sequences. The social network
with stubborn agents is described by the Friedkin-Johnsen (F-J) model where
agents are stubborn to their initial opinions. Firstly, we propose some
sufficient and necessary conditions both in terms of network topology and
system matrix for convergence of the F-J model over single issue. Secondly,
opinion consensus of the F-J model is investigated over issue sequences. Our
analysis establishes connections between the interpersonal influence network
and the network describing the relationship of agents' initial opinions for
successive issues. Taking advantage of these connections, we derive the
sufficient and necessary condition for the F-J model to achieve opinion
consensus over issue sequences. Finally, we consider a more general scenario
where each agent has bounded confidence in forming its initial opinion for
every issue. By analyzing the evolution of agents' ultimate opinions for each
issue over issue sequences, we prove that the connectivity of the
state-dependent network is preserved in this setting. Then the conditions for
agents to achieve opinion consensus over issue sequences are proposed.
Simulation examples are provided to illustrate the effectiveness of our
theoretical results.
