Bipartite consensus of nonlinear multi-agent systems under multi-layer signed graphs

This paper investigates the bipartite leader-following consensus problem for multi-agent systems with nonlinear dynamics and multi-layer signed digraph topologies. According to the structural balance theory, some sufficient conditions are explored for reaching the bipartite leader-following consensus of the multi-layer signed networks by using the pinning control strategy, which are related to the dynamics of the network nodes and the topology of the multi-layer signed network. These conditions are also suitable for traditional single layer signed networks. The numerical example shows the correctness and effectiveness of the proposed method.