Bipartite consensus of matrix-weighted multi-agent systems with dynamic event-triggered mechanism: An adaptive observer-based approach

This paper deals with the bipartite consensus issue for matrix-weighted nonlinear multi-agent systems (MASs). To accurately characterize the multi-dimensional attribute of state connections between agents, matrix weights are utilized to represent the connectivity relationships among agents instead of traditional scalar weights. Additionally, both collaborative and antagonistic interactions are considered on the matrix-weighted networks, which are inscribed with positive and negative semi-definite matrices, respectively. In the development of the distributed control protocol, observers are constructed to estimate the state of agents. Due to the fact that the full states of the nodes of a network are not always available, an observer-based distributed control protocol with matrix weights is constructed to achieve the desirable bipartite consensus. Meanwhile, to avoid using the global information of the communication network, dynamic coupling strengths are designed to obey an adaptive scheme. Also, a novel dynamic event-triggered mechanism is considered for the sake of reducing the communication burden. Based on the assumption that there exists a positive-negative spanning tree in matrix-weighted signed networks, employing algebraic graph theory and Lyapunov stability theory, sufficient conditions are derived to ensure that the matrix-weighted nonlinear MASs can achieve bipartite consensus. Moreover, it is demonstrated that the Zeno phenomenon can be ruled out under the proposed dynamic event-triggered mechanism. Finally, a simulation example is provided to verify the effectiveness of the proposed design method.