Uniform convergence for signed networks under directed switching topologies

Abstract

This paper contributes to developing necessary convergence conditions for directed signed networks subject to cooperative and antagonistic interactions. A class of Laplacian-dependent convergence conditions is presented in the presence of switching topologies. It is shown that the switching signed networks converge monotonically to the intersection space of the null spaces of all Laplacian matrices. Furthermore, the uniform bipartite consensus (respectively, uniform asymptotic stability) of switching signed networks is tied closely to the simultaneous structural balance (respectively, unbalance) of the switching signed digraphs associated with them.