A supply chain system is a complex network of entities including manufacturers, suppliers, distributors and retailers. Since the supply chain system can be seen formally as a cascade nonlinear system and at the same time there are a large number of uncertain parameters such as user demand within that system, a supply chain system can be modelled as a nonlinear cascade system. This paper deals with constructive design problem for nonlinear supply chain inventory systems (SCIS) under certain forms of user demand and the performance of systems subject to unexpected system changes. In order to achieve system stability, a controller will be designed with backstepping method to stabilize the system inventory under uncertain user requirements and a change controller will be designed to bring the performance of the changed system closer to that of the original system. Finally, a numerical simulation example is given to demonstrate the effectiveness of the controller designed using the above method.