Bipartite Consensus Algorithm Under Second-Order Multi-Agent Systems with Matrix Weight-Based Network

Currently, the research on consensus in second-order scalar-weighted multi-agent systems has made significant progress. However, when describing complex problems, scalar weighted networks are difficult to accurately represent the coupling relationships between these problems. The dimensional expansion offered by matrix-weighted networks facilitates the description and analysis of complex issues. Currently, there is still limited research on second-order matrix-weighted networks. In this paper, a novel control protocol is designed using the backstepping method, enabling second-order matrix-weighted networks to achieve bipartite consensus. The impact of the Laplacian's null space on the network's bipartite consensus results is analyzed, and numerical simulations are conducted to validate the conclusions presented in the paper.