Distributed Averaging Problems Over Directed Signed Networks

This article aims at addressing distributed averaging problems for signed networks in the presence of general directed topologies that are represented by digraphs. A new class improved Laplacian potential functions is proposed presenting two notions any digraph: induced unsigned digraph and mirror (undirected) graph, based on which protocols designed using nearest neighbor rules. It shown with protocols, signed-average consensus (respectively, state stability) can be achieved if only associated network structurally balanced unbalanced), regardless whether weight balance satisfied or not. Further, exploited to solve fixed-time topologies, a non-linear protocol ensure bipartite stability within fixed time. Additionally, convergence analyses implemented Lyapunov analysis method, realized revealing tight relationship between behaviors properties functions. Simulation examples presented demonstrate validity our theoretical results networks.