Design of a Delay-based Controller for Fast Stabilization in a Network System with Input Delays via the Lambert W function1

Study of networks with multiple agent dynamics has been a central focus in systems and control community, with numerous results. Among them is the study of how time delays in sensing and actuation could affect network stability, and/or control design for the agents. However, little is known in published work regarding how to design agents' protocols analytically to achieve fast stability reaching. Here, an approach is developed to optimize the rightmost roots of a class of large scale LTI network dynamics via Lambert W function, in order to accomplish this. Results indicate that a delay explicitly present in the controller as a coefficient can create conditions for arbitrary rightmost root assignment. This feature is scalable, can be implemented with ease, and applied effectively for relatively large/small delays.