### 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.

Original language | English |
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Title of host publication | Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications, POSTA 2009 |

Pages | 339-347 |

Number of pages | 9 |

Volume | 389 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009 - Valencia, Spain Duration: 2 Sep 2009 → 4 Sep 2009 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 389 |

ISSN (Print) | 01708643 |

### Other

Other | 3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009 |
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Country | Spain |

City | Valencia |

Period | 2/9/09 → 4/9/09 |

### Fingerprint

### ASJC Scopus subject areas

- Library and Information Sciences

### Cite this

*Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications, POSTA 2009*(Vol. 389, pp. 339-347). (Lecture Notes in Control and Information Sciences; Vol. 389). https://doi.org/10.1007/978-3-642-02894-6_33

**A problem in positive systems stability arising in topology control.** / Knorn, Florian; Stanojevic, Rade; Corless, Martin; Shorten, Robert.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications, POSTA 2009.*vol. 389, Lecture Notes in Control and Information Sciences, vol. 389, pp. 339-347, 3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009, Valencia, Spain, 2/9/09. https://doi.org/10.1007/978-3-642-02894-6_33

}

TY - GEN

T1 - A problem in positive systems stability arising in topology control

AU - Knorn, Florian

AU - Stanojevic, Rade

AU - Corless, Martin

AU - Shorten, Robert

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84883027067&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883027067&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02894-6_33

DO - 10.1007/978-3-642-02894-6_33

M3 - Conference contribution

SN - 9783642028939

VL - 389

T3 - Lecture Notes in Control and Information Sciences

SP - 339

EP - 347

BT - Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications, POSTA 2009

ER -