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In this paper we carry out a stability analysis of a distributed consensusalgorithm in presence of link failures. The algorithm combines a new broadcastversion of a Push-Sum algorithm, specifically designed for handling linkfailures, with a new recursive consensus filter. The analysis is based on theproperties of random Laplacian matrices and random sub-graphs and it may alsobe relevant for other distributed estimation problems. We characterize theconvergence speed, the minimum number of consensus steps needed and the impactof link failures and for both the broadcast Push-Sum and the recursiveconsensus algorithms. Numerical simulations validate the theoretical analysis.

Consensus analysis of random sub-graphs for distributed filtering with link failures