Edge-Event Based Consensus in Networks with Common Time-Varying Delays

This paper studies the delay robustness of a class of periodically edge-event driven synchronous consensus protocols in time-invariant networks. These protocols have the benefits of improved performance at reduced communication and computation costs. Under the assumption that all information links share a common time-varying transmission delay, we give non-conservative estimates of the maximum allowable time-delay and event-detecting period for solving the average consensus problem in terms of the algebraic structure of interaction topologies. Furthermore, rigorous stability analysis shows that the proposed technique is also applicable to the asynchronous consensus with multiple time-delays.