Knorn, Florian and Stanojević, Rade and Corless, Martin and Shorten, Robert
A Problem in Positive Systems Stability Arising in Topology Control.
Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2009) Valencia, Spain, September 2-4, 2009.
Lecture Notes in Control and Information Sciences (LNCIS), 389
Springer Berlin , Heidelberg, pp. 339-347.
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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