In this paper, robustness of PD-like distributive consensus of multiple agents with double-integrator dynamics communicating over a network prone to link failures is discussed. This paper proposes a novel Lyapunov function for stability analysis of double-integrator distributive consensus for a connected topology. In case of non-connected topology the growth of disagreement vector is analyzed using state decomposition. The results obtained for connected and non-connected topologies are then combined to derive a sufficient condition, which guarantees convergence of the agents' states to consensus under switching network topologies. For solving the sufficient condition's concomitant optimization problem, a convex optimization problem is derived which is also of independent interest for any general exponentially stable second-order linear system.
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