On the Boundary Value of the Time-Delay and the Asymptotic Behavior of a Continuous First-Order Consensus Protocol

Coordination in multiagent systems with information influences is studied. In particular, a model of multiagent system in which information is transmitted with a constant delay for all agents is studied. Using the Nyquist criterion applied by Tsypkin for systems with delayed feedback, a formula is obtained for the boundary value of time-delay which is included as a parameter in the system of differential equations with an asymmetric constant Laplacian matrix. The condition of independence of stability from time-delay is founded. The results obtained generalize some previously results and can be applied in coordination analysis in a multiagent systems with complex protocol.