On the general second-order consensus protocol in multi-agent systems with input delays

In this paper we study a general consensus protocol for directed networks of double integrators with input delays. A necessary and sufficient condition is provided, under which not only the consensus is guaranteed but also the agents' states are not exponentially diverging. Based on this condition, the delay robustness of the general protocol is analyzed. The maximal allowable upper bound of the input delay is obtained; the analysis is constructively given and different consensus modes can be regarded as special cases with different parameters. Simulation results are presented to illustrate the effectiveness of the theoretical results.