Linear Consensus Algorithms Based on Balanced Asymmetric Chains

Multi-agent consensus algorithms, with update steps based on so-called balanced asymmetric chains, are analyzed. For such algorithms, it is shown that: (i) the empirical distribution of state values converges asymptotically and (ii) the occurrence of consensus or multiple consensus is directly related to the property of absolute infinite flow of the underlying update chain. An example is provided to illustrate the novelty of the results.