The method of inversion of linear discrete time systems utilizing quantized feedback is examined, and a stability concept is developed. The application in mind is decision feedback equalization (DFE). Sets of necessary conditions and sufficient conditions for stability are derived. A lower bound for the probability of recovery from error, and an upper bound for the mean recovery time are obtained. It is suggested that a stability index for each system could be defined. The bounds derived do not depend on the nature of the noise or the channeli mpulse response except through its length.