<p>This paper discusses two efficient model reduction techniques for large-scale, discrete-time descriptor systems based on Balanced Truncation (BT). Matrix computation plays a major role in these approaches by eliminating the explicit computation of projectors and helps immensely in finding the solution Gramians. The structure-preserving Smith method is proposed in the first place, which exploits the iterative matrix computation to produce the low-rank factors of the Gramians. These low-rank Gramian factors are utilized later to generate the reduced order model (ROM). Secondly, the projected discrete-time Stein equations associated with the discrete-time descriptor system are converted to continuous-time Stein equations by a Cayley transformation. This created a suitable framework for applying the alternative direction implicit (ADI) method to find iterative solutions for the converted continuous-time Stein equations. This paper also presents a mathematical background on exploiting the structure-preserving matrix computation in the ADI approximation to produce low-rank Gramian factors. Finally, simulation results are presented with a comparative analysis to show the accuracy and efficiency of both the MOR approaches.</p>