Skip to main content

Application of Small Gain Type Theorems in Logistics of Autonomous Processes

  • Conference paper
Dynamics in Logistics

Abstract

In this paper we consider stability of logistic networks.We give a stability criterion for a general situation and show how it can be applied in special cases. For this purpose two examples are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Armbruster D, Marthaler DE, Ringhofer C, Kempf K, Jo T (2006) A continuum model for a re-entrant factory. Operations Research 54(5):933–950

    Article  Google Scholar 

  • Dachkovski S, Wirth F, Jagalski T (2005) Autonomous control in shop floor logistics: Analytic models. In: Chryssolouris G, Mourtzis D (eds) Manufacturing, Modelling, Management and Control 2004, Elsevier Science Ltd, Amsterdam, NL

    Google Scholar 

  • Dashkovskiy S, Rüffer B, Wirth F (2005) A small-gain type stability criterion for large scale networks of ISS systems. Proc of 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, pp 5633–5638

    Google Scholar 

  • Dashkovskiy S, Rüffer BS, Wirth FR (2006) An ISS Lyapunov function for networks of ISS systems. In: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, pp 77–82

    Google Scholar 

  • Dashkovskiy S, Rüffer B, Wirth F (2007a) An ISS small-gain theorem for general networks. Mathematics of Control, Signals, and Systems 19:93–122

    Article  MATH  Google Scholar 

  • Dashkovskiy S, Rüffer B, Wirth F (2007b) Numerical verification of local input-to-state stability for large networks. In: Proc. 46th IEEE Conf. Decision and Control, CDC 2007, IEEE, New Orleans, LA, submitted

    Google Scholar 

  • Helbing D, Lämmer S, Witt U, Brenner T (2004) Network-induced oscillatory behavior in material flow networks and irregular business cycles. Physical Review E 70(056118):6 pages

    Google Scholar 

  • Jiang ZP, Teel AR, Praly L (1994) Small-gain theorem for ISS systems and applications. Math Control Signals Systems 7(2):95–120

    Article  MATH  MathSciNet  Google Scholar 

  • Jiang ZP, Mareels IMY, Wang Y (1996) A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica J IFAC 32(8):1211–1215

    Article  MATH  MathSciNet  Google Scholar 

  • Scholz-Reiter B, Jagalski T, de Beer C (2007a) Selbststeuerung logistischer Prozesse in Produktionsnetzen. Industrie Management 23(1):19–22

    Google Scholar 

  • Scholz-Reiter B, Wirth F, Freitag M, Dashkovskiy S, Jagalski T, de Beer C, Rüffer B (2007b) Mathematical models of autonomous logistic processes. In: Hülsmann M, Windt K (eds) Understanding Autonomous Cooperation & Control in Logistics: The Impact on Management, Information and Communication and Material Flow, Springer, Berlin

    Google Scholar 

  • Sontag ED (1989) Smooth stabilization implies coprime factorization. IEEE Trans Automat Control 34(4):435–443

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dashkovskiy, S., Rüffer, B., Wirth, F. (2008). Application of Small Gain Type Theorems in Logistics of Autonomous Processes. In: Kreowski, HJ., Scholz-Reiter, B., Haasis, HD. (eds) Dynamics in Logistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76862-3_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-76862-3_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76861-6

  • Online ISBN: 978-3-540-76862-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics