Practical bipartite synchronization on coupled identical linear systems with antagonistic interactions and time-varying topologies

This paper studies synchronization problem of a network of identical linear systems with antagonistic interactions and time-varying topologies. Assume that the communication graph can be switched among a set of signed graphs, and the following cases may occur: (1) the agents of each signed graph can be divided into two hostile camps, but the members of hostile camps are different; (2) some signed graphs cannot be divided into two hostile camps. We use perturbed analysis to obtain some sufficient conditions for practical bipartite synchronization. Finally, we present a numerical example to illustrate the effectiveness of the obtained results.