Convergence Analysis of Asynchronous Consensus in Discrete-time Multi-agent Systems with Fixed Topology

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.