This paper addresses two related topics. First, a nonrealizable set of input-output equations can be made realizable in the classical state space form by adding a postcompensator whereas this is impossible in the continuous-time case. Construction of such postcornpensator of minimal order is presented. Second, a general subclass of discrete-time systems is suggested, for which the observable subspace is non-integrable. The construction is based on the nonrealizable system, which is realized by adding a postcompensator, and then combined with the output of the original system. (C) 2015 Elsevier Ltd. All rights reserved.