  In order to achieve full detection sensitivity at low frequencies, the
mirrors of interferometric gravitational wave detectors must be isolated from
seismic noise. The VIRGO vibration isolator, called 'superattenuator', is fully
effective at frequencies above 4 Hz. Nevertheless, the residual motion of the
mirror at the mechanical resonant frequencies of the system are too large for
the interferometer locking system and must be damped. A multidimensional
feedback system, using inertial sensors and digital processing, has been
designed for this purpose. An experimental procedure for determining the
feedback control of the system has been defined. In this paper a full
description of the system is given and experimental results are presented.
