Effects of time delay in the synchronized motion of oscillators with Huygens' coupling

In this paper, the well known Huygens' experiment on synchronization is examined, numerically and experimentally, from a control point of view. Namely, a suitable control input is applied to a pair of self-sustained oscillators such that the closed-loop system resembles a pair of oscillators with Huygens' coupling. The case where the interaction between the oscillators and the control input is time delayed is analyzed. In particular, the onset of in-phase and anti-phase synchronization in the coupled/controlled oscillators is studied as a function of the coupling strength and the time delay. An eigenvalue-based numerical test is used as a first step to investigate the stability of the anti-phase synchronized motion and experimental validation is provided