In this paper, the containment control problem for the discrete-time multi-agent systems with first order dynamics is discussed. We first provide the necessary and sufficient condition for containment control without time-delay which is related to the value of the step-size and the structure of the interaction topology through the iterative method. Further, time-delay is taken into account making use of z-transformation and Routh Criterion. Finally, numerical simulations are provided to explain the influence of different step-sizes on stability of the multi-agent systems and testify the obtained results. (C) 2019 Elsevier Ltd. All rights reserved.