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A Problem in Positive Systems Stability Arising in Topology Control

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Positive Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 389))

Abstract

We present a problem in the stability of switched positive systems that arises in network topology control. Preliminary results are given that guarantee stability of a network topology control problem under certain assumptions. Roughly speaking, these assumptions reduce the underlying stability problem to a nonlinear consensus problem with a driving term, that eventually becomes a Lur’e problem. Simulation results are given to illustrate our algorithm. While these results indicate that our assumptions can be removed, a proof of the general stability problem remains open.

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Author information

Authors and Affiliations

  1. Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland

    Florian Knorn, Rade Stanojevic & Robert Shorten

  2. School of Aeronautics & Astronautics, Purdue University, West Lafayette, IN, 47907, USA

    Martin Corless

Authors
  1. Florian Knorn
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  2. Rade Stanojevic
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  3. Martin Corless
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  4. Robert Shorten
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Editor information

Editors and Affiliations

  1. Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camí de Vera s/n, 46022, Valencia, Spain

    Rafael Bru  & Sergio Romero-Vivó  & 

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© 2009 Springer-Verlag Berlin Heidelberg

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Knorn, F., Stanojevic, R., Corless, M., Shorten, R. (2009). A Problem in Positive Systems Stability Arising in Topology Control. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_33

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  • DOI: https://doi.org/10.1007/978-3-642-02894-6_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02893-9

  • Online ISBN: 978-3-642-02894-6

  • eBook Packages: EngineeringEngineering (R0)

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