P.-A. Bliman and G. Ferrari-Trecate. Average consensus problems in networks of agents with delayed communications. Automatica , 44(8):1985--1995, 2008.
The present paper is devoted to the study of average consensus problemsfor undirected networks of dynamic agents having communication delays.By focusing on agents with integrator dynamics, the accent is put here on the study of the time-delays influence: both constant and time-varying delays are considered, as well as uniform and non uniform repartitions of the delays in the network.The main results provide sufficient conditions (also necessary in most cases) for existence of average consensus under bounded communication delays.Simulations are provided that show adequation with these results.