  In this paper, we study a convergence condition for asynchronous consensus
problems in multi-agent systems. The convergence in this context implies the
asynchronous consensus value converges to the synchronous one and is unique.
Although it is reported in the literature that the consensus value under
asynchronous communications may not coincide with the synchronous consensus
value, it has not received much attention. In some applications, the
discrepancy between them may result in serious consequences. For such
applications it is critical to determine under what conditions the asynchronous
consensus value is the same as the synchronous consensus value. We illustrate
these issues with a few examples and then provide a condition, which guarantees
that the asynchronous consensus value converges to the synchronous one. The
validity of the proposed result is verified with simulations.
