Skip to main content
SpringerLink
Log in

Existence and Stability of Limit Cycles in Switched Single Server Flow Networks Modelled as Hybrid Dynamical Systems

  • Conference paper
  • First Online:
Hybrid Systems: Computation and Control (HSCC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1790))

Included in the following conference series:

  • 1738 Accesses

Abstract

The paper deals with the qualitative analysis of the so-called switched flow networks. Such networks are used to model various communication, computer, and flexible manufacturing systems. We prove that for any deterministic network from a specific class, there exists a finite number of limit cycles attracting all the trajectories. Furthermore, we determine this number.

This work was supported by the Australian Research Council

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  1. C. Chase, J. Serrano, and P. Ramadge. Periodicity and chaos from switched flow systems: Contrasting examples of discretely controlled continuous systems. IEEE Transactions on Automatic Control, 38(1):70–83, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. Horn and P.J. Ramadge. A topological analysis of a family of dynamical systems with nonstandard chaotic and periodic behavior. International Journal of Control, 67(6):979–1020, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  3. Z. Li, C.B. Soh, and X. Xu. Stability of hybrid dynamic systems. In Proceedings of the 2-nd Asian Control Conference, pages 105–108, Seoul, Korea, July 1997.

    Google Scholar 

  4. A.S. Matveev and A.V. Savkin. Reduction and decomposition of differential automata: Theory and applications. In T.A. Henzinger and S. Sastry, editors, Hybrid Systems: Computation and Control. Springer-Verlag, Berlin, 1998.

    Google Scholar 

  5. A.S. Matveev and A.V. Savkin. Qualitative Theory of Hybrid Dynamical Systems. Birkhauser, Boston, 1999.

    Google Scholar 

  6. V.V. Nemytskii and V.V. Stepanov. Qualitative theory of differential equations. Princeton University Press, Princeton, New Jersey, 1960.

    MATH  Google Scholar 

  7. J.R. Perkins and P.R. Kumar. Stable, distributed, real-time scheduling of flexible manufacturing/assembly/disassembly systems. IEEE Transactions on Automatic Control, 34(2):139–148, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  8. A.V. Savkin. A hybrid dynamical system of order n with all trajectories converging to (n − 1)! limit cycles. In Proceedings of the 14th IFAC World Congress, Beijing, China, July 1999.

    Google Scholar 

  9. A.V. Savkin and A.S. Matveev. Cyclic linear differential automata: A simple class of hybrid dynamical systems. Automatica, 36(5), 2000.

    Google Scholar 

  10. T. Ushio, H. Ueda, and K. Hirai. Controlling chaos in a switched arrival system. Systems and Control Letters, 26:335–339, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  11. T. Ushio, H. Ueda, and K. Hirai. Stabilization of periodic orbits in switched arrival systems with n buffers. In Proceedings of the 35th IEEE Conference on Decision and Control, pages 1213–1214, Kobe, Japan, December 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, St.Petersburg State University, Bybliotechnaya 2, 198904, St.Petersburg, Petrodvoretz, Russia

    Alexey S. Matveev

  2. Department of Electrical and Electronic Engineering, University of Western Australia, Nedlands, WA, 6907, Australia

    Andrey V. Savkin

Authors
  1. Alexey S. Matveev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrey V. Savkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Matveev, A.S., Savkin, A.V. (2000). Existence and Stability of Limit Cycles in Switched Single Server Flow Networks Modelled as Hybrid Dynamical Systems. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_24

Download citation

  • DOI: https://doi.org/10.1007/3-540-46430-1_24

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation