Event-triggered bipartite consensus of multi-agent systems with switching partial couplings and topologies

Abstract

Bipartite consensus of multi-agent systems with switching communication topologies is addressed in this paper. Neighboring agents are partially coupled with each other and possess cooperative and antagonistic relationships. Moreover, the couplings can vary according to the change of topology. In order to reduce the number of control updates, centralized and distributed event-triggered mechanisms are adopted in designing consensus protocols. Particularly, the given event-triggered conditions are piecewise functions depending on the variable couplings and topologies. Based on the signed graph theory, the error system for bipartite consensus is derived, meanwhile, errors are verified to converge to zero by constructing a suitable Lyapunov function. A union graph is put forward to represent transmission of singe-level state information within a time interval, then bipartite consensus of the multi-agent system is realized if each union graph has a spanning tree. In addition, Zeno behavior is excluded in the presented event-triggered conditions. Numerical examples further validate the obtained theoretical results.