Consensus Dynamics in Continuous High-Order Agent Networks

This paper investigates the consensus problem in higher-order multi-agent systems, focusing on its relationship with graph topology and system parameters. The sufficient and necessary conditions for the attainment of consensus in third-order and fourth-order multi-agent systems are derived. based on the characteristics of the Laplacian matrix and principles of algebraic graph theory. Asymptotic consensus criteria for directed and undirected graphs are proposed through the analysis of the stability of the system matrix. Theoretical results indicate that achieving consensus hinges on the presence of a spanning tree in the graph and relationship between internal/external coupling strengths and Laplacian matrix eigenvalues. Finally, numerical simulations validate the proposed methods.