Distributed accelerating convergence speed of second-order consensus using variable adjacency matrix

In this paper, convergence speed of consensus for a second-order integrator with fixed undirected graph is investigated. To accelerate the speed, a distributed variable adjacency matrix is proposed where the link weights are a function defined based on the distance to the neighbors. The stability of the whole system with a general weight function is shown using a Lyapunov direct method. By using the eigenvalues of the linearized closed-loop system, the speed improvement of the system is validated. The results are verified by simulations.