Two model reducnon schemes ywld an tdenncal reduced model, and one of the methods prowdes an zdentlficatlon algorithm for a two-dtmenswnal pulse response sequence Key Words--Discrete time systems, identification, linear systems, system-order reduction, time-varying systems, stabthty Abstract--Linear, discrete, time-vanable systems are considered, and an important class of uniform reahzations is defined The necessary and sufficient conditions for a pulse response to be uniformly reahzable are obtamed Two model reductmn schemes, one wa balanced realizations and the other wa Hankel matnx are proposed The latter approach can be considered as an ~dent~ficatlon algonthm for the two-dimensional pulse response sequence h(k, 0 It is shown that the two approaches yield an ldentwal reduced model which is always asymptotically stable 1 INTRODUCTION SUBSEQUENT TO Moore's (1981) introduction of balanced reahzatmns, Shokoohi et al (1983, 1984) and Vernest and Kadath (1983) provided general-~zations of balancing to time-variable systems This led to the first systematic procedure to perform model reduction for such systems In this paper, the authors consider discrete tlme-vanable systems and propose two methods to perform model reductton The first method is based on tranforming a system to a balanced coordmate system and the second method is based on a balanced decomposmon of the generahzed Hankel matnx It will be shown that the two approaches will yield an ldenncal reduced model which is always asymptotically stable The second approach, that is, the balanced decomposmon of generahzed Hankel matrix, wdl y~eld an ldent~ficatmn algorithm for reahzmg a ttme-vanable system from a two-&menslonal pulse response sequence h(k, 0 It turns out that there are fundamental differences between the reduced models of continuous and discrete systems The authors wdl address those *