On the stability of positive linear switched systems under arbitrary switching laws

Lior Fainshil*, Michael Margaliot, Pavel Chigansky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider n-dimensional positive linear switched systems. A necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is Hurwitz. Several researchers conjectured that for positive linear switched systems this condition is also sufficient. Recently, Gurvits, Shorten, and Mason showed that this conjecture is true for the case n = 2, but is not true in general. Their results imply that there exists some minimal integer np such that the conjecture is true for all n < np, but is not true for n = np. We show that np = 3.

Original languageEnglish
Pages (from-to)897-899
Number of pages3
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - 2009


  • Metzler matrix
  • Positive linear systems
  • Stability under arbitrary switching law
  • Switched systems

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