  In this two-part paper, we consider multicomponent systems in which each
component can iteratively exchange information with other components in its
neighborhood in order to compute, in a distributed fashion, the average of the
components' initial values or some other quantity of interest (i.e., some
function of these initial values). In particular, we study an iterative
algorithm for computing the average of the initial values of the nodes. In this
algorithm, each component maintains two sets of variables that are updated via
two identical linear iterations. The average of the initial values of the nodes
can be asymptotically computed by each node as the ratio of two of the
variables it maintains. In the first part of this paper, we show how the update
rules for the two sets of variables can be enhanced so that the algorithm
becomes tolerant to communication links that may drop packets, independently
among them and independently between different transmission times. In this
second part, by rewriting the collective dynamics of both iterations, we show
that the resulting system is mathematically equivalent to a finite inhomogenous
Markov chain whose transition matrix takes one of finitely many values at each
step. Then, by using e a coefficients of ergodicity approach, a method commonly
used for convergence analysis of Markov chains, we prove convergence of the
robustified consensus scheme. The analysis suggests that similar convergence
should hold under more general conditions as well.

Systems and Control;Optimization and Control