Control and observability aspects of phase synchronization.

Synchronization phenomena have been studied from a control point of view for many years. However, the vast majority of papers consider complete synchronization, and very few have been devoted to phase synchronization. This paper addresses control and observability aspects of phase synchronization. In order to focus on fundamental aspects, a feedback control framework related to master–slave synchronization is considered. Comparing results using Cartesian and cylindrical coordinates in the context of such a framework and with three known oscillator models, it is argued that (1) observability does not play a significant role in phase synchronization, although it is granted that it might be relevant for complete synchronization, and (2) a practical difficulty is faced when phase synchronization is aimed at, but the control action is not a direct function of the phase error, as it is usually the case in synchronization studies. This difficulty with its fundamental and practical consequences is investigated in some detail. [ABSTRACT FROM AUTHOR]