This paper gives sufficient conditions for the stability of linear descriptor discrete delay systems of the particular form. These new, delay-independent sufficient conditions are derived using approach based on Lyapunov's direct method. This paper, for the first time, offers a general case in the sense that necessity for regularity of system basic matrix A0 is not any more required what was a general assumption in already existing results in literature. The presented method is a typical geometric approach to the problem exposed and avoids needs to transform then system under consideration into the classical discrete descriptor system. In that sense one is capable to see how much should be matrix 0 A stable to overcome instability caused by the time delay matrix 1 A . Numerical example has been working out to show the applicability of results derived.Index Terms-Descriptor time delayed systems, Asymptotic stability, Lyapunov second method I.

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