期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 54, 期 4, 页码 897-899出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2008.2010974
关键词
Metzler matrix; positive linear systems; stability under arbitrary switching law; switched systems
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 n(p) such that the conjecture is true for all n < n(p), but is not true for n = n(p). We show that n(p) = 3.
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