On the Critical Value of Time-Delay in Multiagent Systems

The paper studies the problem of agreement of characteristics in a multiagent system with information influences. In particular, a model of a multiagent system is studied, in which information is transmitted between agents with a constant delay for all agents. For systems with delay, a formula for the critical value of delay with a nonsymmetric matrix is obtained using the Nyquist criterion applied by Tsypkin for a time-delay system. A condition is found under which the stability of the system does not depend on the delay The presented results generalize some of the previously obtained expressions for the time-delay and can be applied to the analysis of agreement of characteristics in a multiagent system with a complex protocol.