Abstract
We address the consensus problem, with a guarantee of connectivity maintenance, for multiagent systems of first- and second-order, communicating over a connected, undirected graph with proximity constraints. Our approach relies on a so-called barrier Lyapunov functions, which encode the distance constraints between pairs of agents. Beyond the consensus algorithms, our primary contribution is to provide strict barrier Lyapunov functions, i.e. positive definite and with negative definite derivative in the agreement subspace. Thus, uniform asymptotic stability of the consensus manifold and the maintenance of the connectivity are guaranteed. Furthermore, with the said barrier functions, we demonstrate the robustness of consensus protocols by establishing global input-to-state stability.
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