Dynamic event-triggered consensus for stochastic delay multi-agent systems under directed topology

This paper addresses the mean-square exponential consensus (MSEC) challenge in stochastic delay multi-agent systems (MASs) under directed topology. The main contributions include avoiding infinitely fast sampling and conducting a random stability analysis. First, a dynamic event-triggered mechanism (DETM) with a fixed positive lower bound for the inter-execution time is designed to prohibit Zeno behavior. The proposed control strategy does not involve the expectations of system signals. Then, sampling errors are estimated using Itô isometry, which ensures that the fixed control at each work interval is maintained with adequate feedback capacity to mitigate the effects of these errors. Furthermore, with the help of a Halanay inequality in integral form and Lyapunov theorem framework, some conditions are proposed to guarantee the consensus of stochastic delay MASs under directed topology. Finally, an example is presented to prove the effectiveness of the DETM method.