A new approach to average consensus problems with multiple time-delays and jointly-connected topologies

This paper investigates average consensus problem in networks of continuous-time agents with delayed information and jointly-connected topologies. A lemma is derived by extending the Barbalatʹs Lemma to piecewise continuous functions, which provides a new analysis approach for switched systems. Then based on this lemma, a sufficient condition in terms of linear matrix inequalities (LMIs) is given for average consensus of the system by employing a Lyapunov approach, where the communication structures vary over time and the corresponding graphs may not be connected. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.