Correction to "D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems" [Dec 2010 2882-2885]

(i) For any x1 ∈ R+, there exists some Kx1 and x1 > 0 such that ∂f2 ∂x2 (x1, t) ≤ − x1 for all t ≥ Kx1 . (ii) For any x2 ∈ R+, there exists some Kx2 and x2 > 0 such that ∂f1 ∂x1 (t, x2) ≤ − x2 for all t ≥ Kx2 . In the following result, which is a correction of Theorem 5.1 in [1], f is required to satisfy the same conditions as in Section V of [1] as well as Assumption A above. Theorem 5.1 Assume that the system ẋ(t) = f(x(t)) has a GAS equilibrium at the origin. Then given any a ∈ R+, there exists v ≥ a with f(v) 0. Proof: If there exist u ≥ a and w ≥ a with f1(u) < 0 and f2(w) < 0 then the sets Ω1, Ω2 in (1) are both non-empty and the argument presented in Theorem 5.1 of [1] implies the existence of a v ≥ a with f(v) 0. We now prove that, provided Assumption A is satisfied, these sets are both non-empty. We shall show that there exists u ≥ a with f1(u) < 0. (The proof that there is a w ≥ a with f2(w) < 0 is identical.) By Assumption A, there exists some constants K, > 0 such that ∂f1 ∂x1 (t, a2) < −