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In this paper we propose an extended version of the Friedkin–Johnsen (FJ) model where we analyze the effects that a homophily-based influence matrix has on the opinion formation process. In particular, we assume that the influence matrix varies over time, and its entries (that represent the appraisals that individuals have of the other individuals) update based on the comparison between their opinions and can take both positive and negative values. This leads to a system of two difference equations, where the first one corresponds to the standard FJ model, except that the influence matrix is no longer constant, and the second one models the dynamics of this matrix. We show that a necessary and sufficient condition for the convergence of this modified version of the classical FJ model is that the influence matrix becomes constant in a finite number of steps. Moreover, we provide the explicit expression for the agents' asymptotic opinions in some special cases: the purely cooperative setting, the case of a structurally balanced network and the case of a single discussion topic. Finally, the case when the topics are correlated and the influence matrix depends on the average opinion vectors is investigated. [ABSTRACT FROM AUTHOR]

In this paper we investigate the herdability property, namely the capability of a system to be driven towards the (interior of the) positive orthant, for linear time-invariant state space models. Herdability of certain matrix pairs (A , B) , where A is the adjacency matrix of a multi-agent network, and B a selection matrix that singles out a subset of the agents (the "network leaders"), is explored. The cases when the graph associated with A , G (A) , is directed and clustering balanced (in particular, structurally balanced), or it has a tree topology and there is a single leader, are investigated. [ABSTRACT FROM AUTHOR]

In this paper we address the consensus problem in the context of networked agents whose communication graph splits into clusters: interactions between agents in the same cluster are cooperative, while interactions between agents belonging to different clusters are antagonistic. This problem set-up arises in the context of social networks and opinion dynamics, where reaching a consensus means that the opinions of the agents in the same cluster converge to the same decision, that is typically different for the different clusters. Under the assumption that agents belonging to the same cluster have the same amount of trust (/distrust) to be distributed among their cooperators (/adversaries), we propose a modified version of DeGroot's law. By simply constraining how much agents in each group should be conservative about their own opinions, it is possible to achieve a nontrivial solution by means of a distributed algorithm. The result is then particularized to unweighted complete communication graphs, and subsequently extended to a class of nonlinear multi-agent systems. [ABSTRACT FROM AUTHOR]