This note deals with the control of production systems that produce many part types with limited capacity. First, a simple model is used to show that the inventory control problem can be solved using modern control theory. A state feedback controller that forces the cumulative production of the system to track precisely the cumulative demand is proposed. The tracking problem is formulated as an H-infinity control problem and the synthesis of the gains of the state feedback controller that guarantees the H-infinity tracking performance of the equivalent dynamics is done by solving a given set of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness of the developed results. The simple model is then extended to include real facts like inspection and processing times.