Continuous-Time Consensus under Persistent Connectivity and Slow Divergence of Reciprocal Interaction Weights

Abstract : In this paper, we present new results on consensus for continuous-time multiagent systems. We introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights. Persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete-time consensus protocols. Slow divergence of reciprocal interaction weights generalizes the assumption of cut-balanced interactions. We show that under these two assumptions, the continuous-time consensus protocol succeeds: the states of all the agents converge asymptotically to a common value. Moreover, our proof allows us to give an estimate of the rate of convergence towards the consensus. We also provide examples that make us think that both of our assumptions are tight.
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https://hal.archives-ouvertes.fr/hal-00839608
Contributor : Antoine Girard <>
Submitted on : Friday, June 28, 2013 - 4:08:57 PM
Last modification on : Thursday, July 4, 2019 - 9:54:02 AM

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Samuel Martin, Antoine Girard. Continuous-Time Consensus under Persistent Connectivity and Slow Divergence of Reciprocal Interaction Weights. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2013, 51 (3), pp.2568-2584. ⟨10.1137/11083438X⟩. ⟨hal-00839608⟩

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