TY - JOUR
T1 - On the stability of positive linear switched systems under arbitrary switching laws
AU - Fainshil, Lior
AU - Margaliot, Michael
AU - Chigansky, Pavel
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Metzler matrix
KW - Positive linear systems
KW - Stability under arbitrary switching law
KW - Switched systems
UR - http://www.scopus.com/inward/record.url?scp=67349123831&partnerID=8YFLogxK
U2 - 10.1109/TAC.2008.2010974
DO - 10.1109/TAC.2008.2010974
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AN - SCOPUS:67349123831
SN - 0018-9286
VL - 54
SP - 897
EP - 899
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
ER -