A Problem in Positive Systems Stability Arising in Topology Control

  • Florian Knorn
  • Rade Stanojevic
  • Martin Corless
  • Robert Shorten
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 389)


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.


Average Matrix Topology Control Positive System Geometric Graph Consensus Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Florian Knorn
    • 1
  • Rade Stanojevic
    • 1
  • Martin Corless
    • 2
  • Robert Shorten
    • 1
  1. 1.Hamilton InstituteNational University of Ireland MaynoothMaynoothIreland
  2. 2.School of Aeronautics & AstronauticsPurdue UniversityWest LafayetteUSA

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