On Stability of Uncertain Time-Delay Systems: Robustness Margin for the Inventory Control

This paper concerns robust stabilization of an inventory control problem of uncertain time-delayed systems. The case study concerns the inventory control, under uncertainties on the lead times of production. The customer demand 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 proposed control law is based on a saturated feedback predictor structure. The end customer demand is considered as the external perturbation. The results give the necessary and suf?cient conditions on the existence of robust control. A new robustness margin condition using an invariant interval on the prediction is then formulated. The results demonstrate that it possible to improve the performances of the production system by choosing optimally the control parameters and the speci?cations of the production system.