Abstract This paper investigates a biased average error for distributed average consensus problems under asynchronous updates in the expectation sense. The asynchronism in this context implies no existence of a global clock as well as random characteristics in communication uncertainty such as communication delays and packet drops. Although some previous works contributed to the design of average consensus protocols to guarantee the convergence to an exact average, these methods may increase computational burdens due to extra works. Sometimes it is thus beneficial to make each agent exchange information asynchronously without modifying the algorithm, which causes randomness in the average value as a trade-off. In this study, an expected average error is analyzed based on the switched system framework, to estimate an upper bound of the asynchronous average compared to the exact one in the expectation sense. Two different numerical examples, distributed sensor fusion and opinion dynamics, are provided to validate the proposed results.
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