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Adding and removing nodes in consensus

The distributed consensus problem has been widely studied in the literature, either with fixed and with time-varying topologies. Typically, the set of agents involved in the consensus does not vary over time. In this paper the possibility to dynamically add or remove nodes during consensus is investigated. Specifically, a framework for the achievement of consensus while dynamically adding nodes to the network is provided, together with a stability condition. Moreover, the effects of removing a single node in the network at a given time instant are inspected, characterizing the difference between the asymptotic values with and without the removed node, depending on the removal time instant. A further result provided in this paper is the relation between the node removal at a given time instant and the initial removal of that node (i.e., at the initial time step).