Synchronization analysis of coupled identical linear systems with antagonistic interactions and time-varying topologies

The paper investigates bipartite synchronization (BS) and bounded bipartite synchronization (BBS) of a network of identical linear systems with antagonistic interactions and time-varying topologies. When at each time instant all agents can be divided into two hostile camps, and the members of two hostile camps are unchanged as time goes on, we obtain some sufficient conditions for bipartite synchronization under mild assumption that the signed graph is uniformly quasi-strongly connected. When the members of hostile camps are changed as time goes on, or at some time instants all agents cannot be divided into two hostile camps, we consider this network as a perturbation of a particular network which can achieve bipartite synchronization. We obtain some sufficient conditions such that the network achieves bounded bipartite synchronization. Finally, we present two numerical examples to illustrate the effectiveness of the obtained results.