Uniform convergence for directed time-varying signed networks under generalized Laplacian-class model

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This paper addresses the uniform convergence problems for signed networks under directed time-varying topologies. A generalized Laplacian-class model is proposed by admitting the time-varying relative self-effect of each agent, which can be reflected by a newly introduced notion of the diagonal dominance degree. With a state transition matrix-based approach, sufficient conditions on uniform asymptotic stability and uniform bipartite consensus subject to any initial time are obtained for signed networks, respectively. It is shown that these uniform convergence behaviors depend on not only the topology structure but also the diagonal dominance degree. The uniform convergence results for time-varying signed networks are further applied to cope with the uniform asymptotic stability problem of general linear time-varying systems.