Stabilization of supply networks with a varying manager-reaction time delay

This paper investigates the stabilizing strategies of a supply network system by taking into account the varying reaction time delay of the manager. A feedback control law is designed to realize the stabilization of such a network. Then, sufficient conditions for the design of a control strategy to stabilize the supply network are obtained based on the Lyapunov–Krasovski functional and the robust control method. These sufficient conditions are given in terms of linear matrix inequalities. Moreover, the robust H∞ disturbance performance for the supply network subject to unknown demand is also established. A numerical study is provided to verify the effectiveness of the proposed method.