Second-order consensus of multiagent systems with matrix-weighted network

Abstract

This paper studies second-order consensus problem on the matrix-weighted undirected network, which is a generalization of second-order scalar-weighted network. The matrix coupling can describe the interdependencies of multi-dimensional states among agents. To highlight the influence of matrix coupling, we analyze the double integral model in matrix-weighted multiagent system network. A sufficient and necessary algebraic condition based on coupling strength, matrix theory and Lyapunov stability theory is established to achieve second-order consensus. With aid of the established property, a fairly straightforward algebraic graph condition is obtained, which ensures that the matrix-weighted multiagent system achieves second-order consensus. Moreover, owing to the existence of positive semi-definite connections, the clustering phenomena naturally exists, which shows that matrix coupling plays an important role in the convergence of the matrix-weighted multiagent system network. And an algebraic graph condition for finding all clusters is offered, which can guarantee the desired number of clusters via designing matrix-weights in practical applications. Finally, four simulation examples are given to illustrate the effectiveness of the obtained results.