This paper discusses stability analysis supply chain dynamics using feedback control law structure. The case study concerns the inventory control system which is considered as an input-delay system under uncertainties on customer demands with constraints related to losses of stored products. Due to the lead time of the control law and factors such as the customer demand which is supposed to be unknown, the objective is to define a control law which permits to satisfy the end-customer demand and for which the production system requirements will be completely met. The end customer demand is considered as the external perturbation. To study the stability analysis, two types of control law are proposed, both based on a feedback predictor structure. The necessary and sufficient conditions on the existence of control law are then formulated. The results demonstrate that it possible to improve the performances of the supply chain by choosing optimally the control parameters and the specifications of the production system.