Optimal Delay-Dependent H ∞infinity Control for Closed-Loop Supply Chain System with Multiple Delays

This paper proposes a dynamic model of a closed-loop supply chain system with remanufacturing delay and disposal delay. A mixed algorithm combining immune genetic algorithm and linear matrix inequality method is designed for achieving the globally optimal performance of H_∞ control for the closed-loop supply chain system. The study shows that the globally optimal performance of the system deteriorates gradually with the increase of time delay and the influence of remanufacturing delay to the system performance is greater than that of the disposal delay. Numerical example shows that the uncertain impact of the supply chain system can be restrained by the delay-dependent H_∞ control strategy so that the closed-loop supply chain system can remain stable.