화학공학소재연구정보센터
IEEE Transactions on Automatic Control, Vol.54, No.4, 897-899, 2009
On the Stability of Positive Linear Switched Systems Under Arbitrary Switching Laws
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.