Stability analysis of logistics networks with time-delays

Logistics network represents a complex system where different elements that are logistic locations interact with each other. This interaction contains delays caused by time needed for delivery of the material. In this paper, we study local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. An appropriate Lyapunov-Razumikhin function and the small gain condition are utilized to establish some conditions for stability analysis of the network under consideration. Our stability conditions for the logistics network are based on the information about the interconnection properties between logistic locations and their production rates. Finally, numerical results are provided to demonstrate an application of the proposed approach.