Currently, in view of the fact that almost all the tasks of the practice of controlling CNC machine and robot drives cannot be accurately represented by linear models, and there is no solution to non-linear models in the general case, a very important task is to develop control algorithms based on discrete models. Discrete models of nonlinear systems assume variable state, control, and measurement matrices that determine an infinite number of variants of this model. Therefore, some tool is needed to calculate the degree of adequacy of mathematical models and real objects. The paper considers theoretical statements related to the main directions of research in the field of theoretical issues - the study of the dynamics of CNC machine and robot drives and their modeling. The paper studies the drives of CNC machine and robots by the criterion of identifiability based on a discrete digital control model. Criteria of observability, controllability and identifiability of drives are considered as a function of the rank of an extended state matrix with a measurement matrix, in which the relative errors of the information-measuring system are analytically taken into account. An algorithm for calculating the identifiability criterion for a nonlinear control system in a discrete linearization version is proposed. It is proposed to use identification in terms of the correspondence of the mathematical model to the results of the operation of the object. Drive control by means of a discrete vector-matrix algorithm involves the calculation of the state matrix at each step. Therefore, at each step, the determinant of the extended matrix is calculated, which is compared with a constant that numerically divides the space of the state matrices. Thus, the operation of the drives itself makes it possible to determine its identifiability. As a criterion for the optimality of the identification algorithm, a decision-making optimality criterion is chosen in combination with an identifiability criterion for an optimal control algorithm by the criterion of minimum quadratic form. The vector-matrix model of drives in the state space is presented taking into account the relative accuracy of measuring the state of the information-measuring subsystem of drives. It is proposed for practical problems to determine the identifiability criterion by modeling the state matrix for cases when the state matrix parameters exit the space of realizable parameters of serviceable drives. The linearized model of CNC machine and robot drives has limitations in accordance with technical characteristic, for example, restrictions on the strength of electric current and voltage. The obtained research results can be used to build diagnostic systems for CNC machine and robot drives.