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A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays

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  • Sergey Dashkovskiy
  • Hamid Karimi
  • Michael Kosmykov

Abstract

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. Complexity of the system, time-delays and perturbations in a customer demand may cause unstable behaviour of the network. This leads to the loss of the customers and high inventory costs. Thus the investigation of the network on stability is desired during its design. In this article we consider local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. We are looking for verifiable conditions that guarantee stability of the network under consideration. Lyapunov–Razumikhin functions and the local small gain condition are utilised to obtain such conditions. 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 the proposed approach.

Suggested Citation

  • Sergey Dashkovskiy & Hamid Karimi & Michael Kosmykov, 2012. "A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(5), pages 845-853.
    • Handle: RePEc:taf:tsysxx:v:43:y:2012:i:5:p:845-853
    DOI: 10.1080/00207721.2010.528179
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    Cited by:

    1. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    2. N. Noroozi & A. Khayatian & S. Ahmadizadeh & H.R. Karimi, 2016. "On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(7), pages 1598-1614, May.
    3. Jens Heger & Torsten Hildebrandt & Bernd Scholz-Reiter, 2015. "Dispatching rule selection with Gaussian processes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(1), pages 235-249, March.

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