Correction to “D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems”

Abstract—We correct some errors in the statements and proofs presented in Section V of the above mentioned manuscript. In the recent paper [1], the results of Section V are incorrect as stated. In this brief note, we first present an example to show that the statement of Theorem 5.1 in [1] is incorrect and then state a corrected version of this result under an additional technical assumption on the vector field . Example 1: Consider the 2-D cooperative system given by Using a similar argument as employed in Example 3.19 of [2], it can be shown that the origin is a globally asymptotically stable equilibrium of this system. However, it is clear that choosing , there can be no vector with . The proof of Theorem 5.1 in [1] implicitly assumes that for any , both of the set