The region of convergence of the differential model of consensus

This paper is devoted to consensus problems in continuous multi-agent systems whose corresponding Kirchhoff matrix is diagonalizable and $0$ is a simple eigenvalue of $L$. It is proved that the limiting matrix of the solution of the system of linear differential equations satisfying the initial condition is a eigenprojection of the Kirchhoff matrix $L$, which also determines and is defined the region of convergence to consensus of the DeGroot algorithm.