Multi-agent consensus with diverse time-delays and jointly-connected topologies

This paper investigates consensus problems in networks of continuous-time agents with diverse time-delays and jointly-connected topologies. For convergence analysis of the networks, a class of Lyapunov–Krasovskii functions is constructed which contains two parts: one describes the current disagreement dynamics and the other describes the integral impact of the dynamics of the whole network over the past. By a contradiction approach, sufficient conditions are derived under which all agents reach consensus, even though the communication structures between agents dynamically change over time and the corresponding graphs may not be connected. The obtained conditions are composed of a sum of decoupled parts corresponding to each possible connected component of the communication topology. Finally, numerical examples are included to illustrate the obtained results.