Stability of Human-in-the-Loop Multiagent Systems with Time Delays

We study a group of agents with linear time-invariant (LTI) dynamics commanded by a human operator with a general LTI model and a reaction time-delay. Under remote operation, the human receives time-delayed information from a subset of the agents, and commands, under another time-delay, the same or a different subset of the agents. Stability of this human-in-the-loop multiagent system is next studied both in “time-domain” and “frequency-domain”, specifically to investigate how the system network graph affects the largest delay tolerable before losing stability. In a case study, system stability is shown to hold for larger delays in graphs with fewer edges than in a strongly-connected graph.