A digital control system is probably the best technical solution to the problem of automatic control of the Virgo interferometric antenna for gravitational wave detection, provided that very critical specifications concerning residual noise introduced by the digital system in the measurement band are met. For this purpose, a model of the digital system has been developed and tested to quantify the main sources and levels of noise. Experimental measurements, obtained using a prototype of the automatic control system, and theoretical analysis of the performances of the digital control loops have demonstrated the feasibility of a digital control system.