Bipartite consensus for a class of double-order multi-agent systems with time-varying delays on antagonistic interactions

Abstract

In this paper, the bipartite consensus problems are investigated for multi-agent systems with double-integrator dynamics and antagonistic interactions. We consider bipartite consensus under the given protocol, which means that the absolute value of the position is the same when all the velocities of agents are 0, but the sign may be opposite. When there are no delays, the necessary and sufficient condition is derived for the system to asymptotically achieve the bipartite consensus under the given protocol. With the existence of communication delays, a sufficient condition is also obtained for the system to asymptotically achieve the bipartite consensus.