Delay-dependent coupling for a multi-agent LTI consensus system with inter-agent delays

• Dynamics in which agents aim to reach consensus.
• Agents communicate under delays, which can destabilize the network.
• Delay-dependent coupling (DDC) is proposed to prevent instability.
• With DDC, agent couplings are adjusted explicitly by delays.

Delay-dependent coupling (DDC) is considered in this paper in a broadly studied linear time-invariant multi-agent consensus system in which agents communicate with each other under homogeneous delays, while attempting to reach consensus. The coupling among the agents is designed here as an explicit parameter of this delay, allowing couplings to autonomously adapt based on the delay value, and in order to guarantee stability and a certain degree of robustness in the network despite the destabilizing effect of delay. Design procedures, analysis of convergence speed of consensus, comprehensive numerical studies for the case of time-varying delay, and limitations are presented.