On the existence of a nonpositive solution to the Riccati equation

The purpose of this correspondence is to correct a claim of [1]. Reference [1, theorem 4] states a necessary and sufficient frequency-domain condition for the existence of a nonpositive definite solution to the algebraic Riccati equation. This condition is, however, not correct, since the stated condition is necessary but not sufficient. This will be demonstrated by means of a counterexample.