Consensus analysis for multi-agent systems with asynchronous sampling and time delays: A time translation method

This paper addresses the consensus problems in multi-agent systems with asynchronous sampling and time delays. A key challenge in such systems is the combined impact of asynchronous sampling and time delays. Analyzing the synchronization of agents’ states becomes more complicated due to these practical issues in distributed control, in contrast to the traditional networked systems generally based on synchronous sampling. To overcome this difficulty, the paper employs a time translation method to virtually synchronize the asynchronous sampling sequences of all agents. However, this sampling-synchronization introduces additional time delays into the virtual system. Additionally, an integral-based periodic event-triggered mechanism is introduced, where each agent periodically checks its local event-triggering condition to determine when to interact with its neighbors. This ensures that communication occurs only when necessary, and reduces unnecessary data transmissions. Based on Lyapunov functions and Barbalat’s Lemma, the consensus conditions of the sampling-synchronized system via time translation with time delays are derived.