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In this two-part paper, we consider multicomponent systems in which eachcomponent can iteratively exchange information with other components in itsneighborhood in order to compute, in a distributed fashion, the average of thecomponents' initial values or some other quantity of interest (i.e., somefunction of these initial values). In particular, we study an iterativealgorithm for computing the average of the initial values of the nodes. In thisalgorithm, each component maintains two sets of variables that are updated viatwo identical linear iterations. The average of the initial values of the nodescan be asymptotically computed by each node as the ratio of two of thevariables it maintains. In the first part of this paper, we show how the updaterules for the two sets of variables can be enhanced so that the algorithmbecomes tolerant to communication links that may drop packets, independentlyamong them and independently between different transmission times. In thissecond part, by rewriting the collective dynamics of both iterations, we showthat the resulting system is mathematically equivalent to a finite inhomogenousMarkov chain whose transition matrix takes one of finitely many values at eachstep. Then, by using e a coefficients of ergodicity approach, a method commonlyused for convergence analysis of Markov chains, we prove convergence of therobustified consensus scheme. The analysis suggests that similar convergenceshould hold under more general conditions as well.

Distributed Algorithms for Consensus and Coordination in the Presence of  Packet-Dropping Communication Links - Part II: Coefficients of Ergodicity  Analysis Approach