State synchronization in local-interaction networks is robust with respect to time delays

This is among the first results that suggest that multi-agent systems that interact through time-invariant, nearest-neighbor rules, can synchronize their states regardless of the size of communication delays. Network connectivity and consistency in the use of neighbor state information is all that is needed. The analysis in this paper is performed in discrete time and is based on the properties of non-negative matrices. Due to the fact that the state transition matrix is no more ergodic, the results of [1] cannot be applied. A crucial observation regarding the delayed dynamics allows the reduction of the model and the establishment of ergodicity for the system’s state transition matrix.