In this paper, the problem of time-varying output tracking is studied in discrete-time descriptor systems. The descriptor system is subject to practical constraints such as input saturation and exogenous disturbances and consists of algebraic equations besides the difference equations in system modeling. The control problem is solved by proposing an observer-based composite nonlinear feedback controller to attain a suitable response and desired performance. The proposed control law is designed based on estimated states from a full-order descriptor observer. Considering the nonlinearity behavior and complicated analysis procedure, a theorem is dedicated to studying the closed-loop system that looks into the operation of the proposed observer-based control law upon different cases of the saturation function. It is demonstrated that the proposed control law is capable of working even if the saturation occurs. Furthermore, ultimate boundedness analysis is also done to verify the performance of the proposed control law in the presence of exogenous disturbance. The accuracy of theoretical achievements is endorsed by computer simulations through a numerical example and a practical example (a hydraulic tank system). (C) 2020 Elsevier Ltd. All rights reserved.