Abstract
This paper investigates the effect of asynchronous communications on stationary solutions for discrete-time multiagent systems with a fixed topology. The asynchrony in this context implies that there is no global clock to synchronize the update time in each distributed agent and also each agent updates its own state asynchronously without waiting for values received from neighboring agents. It has been noted without much attention that asynchronous stationary solutions may not be unique and disagree with a synchronous stationary value. In some applications, this discrepancy may cause serious consequences, and thus it is critical to analyze the effect of asynchrony on stationary solutions. In this paper, we develop necessary and sufficient conditions for the uniqueness of stationary solutions for discrete-time multiagent systems. In the case of nonunique stationary solutions, the normalized expected error between synchronous and asynchronous stationary solutions is also analyzed. To validate the proposed methods, we provide three example problems: 1) containment control; 2) fixed-point iteration; and 3) distributed averaging formulated in a discrete-time setting.
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