Fully distributed consensus of discrete-time linear multi-agent systems with large input and communication delays

This paper investigates the consensus problem for discrete-time leader-following multi-agent systems subject to large time delays. Building upon two assumptions, a novel fully distributed protocol is devised by utilizing a normalized weighting matrix, depending solely on the relative output measurement. It is shown that, for arbitrarily large yet bounded input and communication delays that are constant and exactly known, the consensus problem can be effectively addressed by both the proposed protocol and its truncated version. Assuming further that followers incorporate solely input delays, then the permitted delays can be time-varying and different. The proposed protocols do not rely on global information of the directed communication topology, thus ensuring robustness against alterations in the communication topology. A numerical example is employed to validate the effectiveness of the suggested approach.