This paper is concerned with strong delay-independent stability of linear time-invariant (LTI) systems with a single time-delay. Stability analysis of linear delay-systems is complicated by the need to locate the roots of a transcendental characteristic equation. In this paper we propose a convex necessary and sufficient condition for strong delay-independent stability. This result mainly follows from the Kronecker sum properties and the Kalman-Yakubovich-Popov lemma, which allows us to present the main result in terms of a single linear matrix inequality (LMI) feasibility test. The result is illustrated by simple numerical examples. (C) 2017 Elsevier Ltd. All rights reserved.