Stability of interval positive continuous-time linear systems

It is shown that the convex linear combination of the Hurwitz polynomials of positive linear systems is also the Hurwitz polynomial. The Kharitonov theorem is extended to the positive interval linear systems. It is also shown that the interval positive linear system described by state equation (x) over dot = Ax, A is an element of R-nxn, A(1) <= A(1) <= A(2) is asymptotically stable if and only if the mitrices. A(k) = 1, 2 are Hurwitz Metzler matrices.