Distributed Consensus on Set-valued Information

Abstract

This paper focuses on the convergence of infor- mation in distributed systems of agents communicating over a network. The information on which the convergence is sought is not represented by real numbers, rather by sets of real numbers, whose possible dynamics are given by the class of so-called Boolean maps, involving only unions, intersections, and complements of sets. Based on a notion of contractivity, a necessary and sufficient condition ensuring the global and local convergence toward an equilibrium point is presented. In particular the analysis of global convergence recovers results already obtained by the authors, but the more general approach used in this paper allows analogue results to be found to characterize the local convergence.