Abstract
In this paper, we analyze a given production network in view of stability, which means boundedness of the state of the network over time. From a mathematical point of view we model the network by differential equations. With help of local input-to-state stability (LISS) Lyapunov functions and a small gain condition we check, if the network is stable. This results in the derivation of conditions for the production rates for which stability of the production network is guaranteed.
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References
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Acknowledgments
This research is funded by the German Research Foundation (DFG) as part of the Collaborative Research Centre 637 “Autonomous Cooperating Logistic Processes: A Paradigm Shift and its Limitations” (SFB 637).
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Dashkovskiy, S., Görges, M., Naujok, L. (2011). Local Input-to-State Stability of Production Networks. In: Kreowski, HJ., Scholz-Reiter, B., Thoben, KD. (eds) Dynamics in Logistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11996-5_8
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DOI: https://doi.org/10.1007/978-3-642-11996-5_8
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