This document describes the result of an exploratory research that led to structuring a review categorizing and subcategorizing the Z transform and its applications in control systems. For the above, the method by indexes or based on a categorical taxonomy oriented by sources classified with the keys is used: history, conceptualization, application in elementary signals, criteria and constructive characteristics, and analysis and design in digital systems; the methodology is validated by the judgment of experts from the SciBas research group. Finally, an application is developed in MatLab® simulating an implementation of a control system. As a consequence, a knowledge base line is established for research on applications based on the Z transform, and a way of approaching simulations as an alternative to validate results in a particular case of control systems.