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In this technical note, an analytical framework for studying the dynamics of perishable inventory systems is developed using control-theoretic approach. In the considered systems, the deteriorating stock at a goods distribution center is used to fulfill unknown, time-varying demand. The stock is replenished using multiple supply options characterized by different lead-time delay. In contrast to the classical stochastic, or heuristic approaches, a formal design procedure based on discrete-time linear-quadratic (LQ) optimal control is employed. The analytically derived suboptimal controller satisfies positivity constraints and ensures full demand satisfaction for any bounded demand pattern. Moreover, a methodology for analysis of parametric uncertainties is elaborated, and another, nonlinear controller that guarantees robustness to uncertain delay variations is designed.