Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate L-2-stability for such a class of systems. Sufficient conditions, and in some particular cases, necessary and sufficient conditions for exponential L-2-stability are established, for multivariable systems with commensurate or rationally independent delays. An analysis of discontinuities evolution appearing in the system response is proposed. Finally, a robustness issue is discussed for time-varying delays. (C) 2014 Elsevier Ltd. All rights reserved.