Responsible-Eigenvalue Control for Creating Autonomy in Coupled Systems With Delays

A class of linear time-invariant (LTI) consensus system with multiple agents and identical communication delays among the agents is considered. For this type of system, we recently showed that a responsible eigenvalue (RE) exists determining the amount of delay (delay margin) that the system can withstand without losing stability. In this paper, we use RE to design controllers such that the delay margin of the system increases as the agents make autonomous decisions. This Responsible Eigenvalue-control enables real-time tuning of RE in a way that the system becomes robust against delays. A numerical example demonstrates intriguing results that connect for the first time in the literature the controller design, the features of the associated graph Laplacian, and RE concept.