Convergence analysis for a class of nonlinear consensus algorithms

In this paper, sufficient conditions for the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents are proposed. More precisely, in the consensus algorithms studied here, the control input of each agent is assumed to be a state-dependent combination of the relative positions of its neighbors in the information flow graph. It is shown that under some mild assumptions, the contraction of the convex hull of the agents can be guaranteed. A set-valued Lasalle-like approach is then employed to derive the convergence from the contracting property. The proposed convergence criteria are verified for two different consensus algorithms via simulations.