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Finite-time consensus on the median value by discontinuous control

In this paper we propose a novel protocol to solve the consensus on the median value problem, i.e., the decentralized agreement problem for networked multi-agent systems where the quantity of interest is the median value as opposed to the average value of the agents' states. The median value is a statistical measure particularly robust to the existence of outlier agents which are a significant issue in large scale averaging networks. The proposed protocol achieves consensus on the median value in finite time by exploiting a discontinuous local interaction rule.