  We study, both analytically and numerically, the dynamics of mechanical
oscillators kept in motion by a feedback force, which is generated
electronically from a signal produced by the oscillators themselves. This kind
of self-sustained systems may become standard in the design of
frequency-control devices at microscopic scales. Our analysis is thus focused
on their synchronization properties under the action of external forces, and on
the joint dynamics of two to many coupled oscillators. Existence and stability
of synchronized motion are assessed in terms of the mechanical properties of
individual oscillators --namely, their natural frequencies and damping
coefficients-- and synchronization frequencies are determined. Similarities and
differences with synchronization phenomena in other coupled oscillating systems
are emphasized.
