Distributed algorithm for dissensus of a class of networked multiagent systems using output information

Dissensus Algorithms for Opinion Dynamics on the Sphere

“…In [9], dissensus is described as bipartite consensus, and linear/nonlinear consensus protocols can be applied to achieve stable dissensus on a signed graph with negative weights representing antagonistic relationships and positive weights representing collaborative relationships. In [10], a distributed algorithm is developed to reach dissensus for a multi-agent system on a signed digraph. These dissensus behaviors mostly appear in signed graphs, but not in unsigned graphs.…”

“…Remark IV.6 In Theorem IV.1 and Theorem IV.5, we have shown that the PCA-based opinion dynamics (8) yields unstable consensus and stable dissensus, respectively, for a 2−agent system on an unsigned graph. This result cannot be achieved by the averaged dissensus algorithms since they require the graph to be signed and weighted, and result in stable dissensus for such a graph [9], [10]. The averaged consensus algorithm on the unit sphere, however, can only lead to stable consensus with positive interaction matrix (i.e., unsigned graph), and lead to stable dissensus with signsymmetric interaction matrix (i.e.…”