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In this brief, a linear-matrix inequality (LMI) based strictly-positive-real (SPR) characterization and its application to absolute stability problem for discrete-time descriptor systems is addressed. After giving the definition of SPR, the Cayley transformation is used to establish formulas bridging the admissible descriptor form realizations for SPR and strictly-bounded-real transfer matrices. Based on these, an LMI-based necessary and sufficient condition for a descriptor system to be, simultaneously, admissible and SPR is derived. The obtained result is further applied to the absolute stability problem involving a linear time-invariant descriptor system and a memoryless time-varying nonlinearity. Numerical tractability of the results are illustrated by two examples.