This paper is concerned with the network-based practical set consensus problem of multi-agent systems subject to input saturation constraints. Considering network-induced delays, data quantization and aperiodic sampling intervals, a network-based framework which allows each agent to be remotely controlled over the communication network is established. Under this framework, a new network-based consensus protocol with input saturation constraints is proposed. With this protocol, the consensus problem can be transformed into the stabilization problem of time-delay systems with bounded perturbations. By using the Lyapunov-Krasovskii approach, a stability condition guaranteeing that the error system can exponentially converge to a bounded set is derived, where the region of initial conditions can be estimated by considering the effect of the first delay interval. Based on this stability condition, the network based consensus controller gain matrix can be obtained. An optimization algorithm is introduced for simultaneously designing the consensus controller gain and estimating the region of attraction as small as possible and the region of initial conditions as large as possible. A numerical example is given to illustrate the efficiency of all the results derived in this paper. (C) 2017 Elsevier Ltd. All rights reserved.