In this paper, the authors study the asymptotic behavior of solutions of difference equations which arise in certain control systems. What makes their analysis unusual is that, in effect, small perturbations are allowed in the shift of the independent variable, discrepencies which correspond to infinitesimal desynchronizations in the original physical problem. The reviewer has seen no other such results and is very curious about how they were obtained, since no proofs are given in the paper. The proofs for the situation where the shifts are all the same--this is the case of ordinary difference equations--are highly technical, and must depend on a complete asymptotic analysis of the difference equation. The dearth of supporting information in the paper is not alleviated by the the bibliographical entries, which consist of only two books: Gantmakher’s well-known book on matrices [1] and another Russian work on the approximate solution of operator equations [2]. The reviewer hopes that the recent appearance of similarly autonomous mathematical papers from the Soviet Union does not signal a return to those dark times when Western and Soviet mathematics operated independent of each other.