On the asynchronous bipartite consensus for discrete-time second-order multi-agent systems with switching topologies

The asynchronous bipartite consensus for a group of agents with second-order dynamics is examined in this paper, where the asynchrony means that the time instants when each agent receives the neighbors' data information are completely independent of other agents'. The communication among the agents is described by a time-varying signed and structurally balanced digraph, which is equivalent to assuming that the agents can be divided into two groups without any common agents, in which the agents within the same group are cooperative and the agents between different groups are competitive. An asynchronous distributed control protocol is designed to implement the bipartite consensus. By using the product properties of row-stochastic matrices from a noncompact set, a sufficient condition can be established under a loose assumption that is the union of communication topologies related to any time intervals with given length has a spanning tree. Finally, a simulation instance is provided to verify the reachability of asynchronous bipartite consensus.