Title: Control and Observability Aspects of Phase Synchronization,
Abstract: This paper addresses important control and observability aspects of the phase
synchronization of two oscillators. To this aim a feedback control framework is
proposed based on which issues related to master-slave synchronization are
analyzed. Comparing results using Cartesian and cylindrical coordinates in the
context of the proposed framework it is argued that: i)~observability does not
play a significant role in phase synchronization, although it is granted that
it might be relevant for complete synchronization; and ii)~a practical
difficulty is faced when phase synchronization is aimed at but the control
action is not a direct function of the phase error. A procedure for overcoming
such a problem is proposed. The only assumption made is that the phase can be
estimated using the arctangent function. The main aspects of the paper are
illustrated using the Poincaré equations, van der Pol and Rössler
oscillators in dynamical regimes for which the phase is well defined.