Event-based consensus for second-order nonlinear multi-agent systems with matrix-weighted signed networks

This paper investigates the bipartite consensus problem of multi-agent systems (MASs) with matrix-weighted interactions, functioning on undirected signed graphs. To decrease communication loss, the event-triggered mechanism is incorporated into the proposed bipartite consensus protocol. To prove bipartite consensus, two auxiliary variables are introduced to make the proof simpler. The adaptive technique is utilized to reduce the impact of nonlinear factors, and Lyapunov theory is employed to establish the stability of error systems and verify their performance over time. The proposed controller allows the MASs to reach exponentially bipartite consensus. Furthermore, it can be demonstrated that the method prevents the occurrence of an infinite sequence within a finite time interval, ensuring that Zeno behavior is avoided. Finally, a series of simulations are presented to validate and reinforce these theoretical results.