Stabilization of multi-agent systems via distributed difference feedback control

Difference feedback control (DFC) uses the difference between the current state (output) and some delayed state (output) to compensate the feedback loop of the system. It does not alternate the original equilibrium of the system and thus can be used for stabilization of systems with unknown steady states. In this paper we extend the idea of DFC to network-based multiagent systems with sufficiently large input or communication delays. An explicit design scheme is provided for choosing the parameters of distributed difference feedback controller (DDFC). By taking the self-delays of DDFC as some commensurate values of input delays of the multi-agent systems, it is shown that the first-order integer system with any large diverse input delays and communication delays can be stabilized by DDFC. The result is applied to the synchronization of a network of Kuramoto oscillators with diverse input delays.