The paper is concerned with the L2-stability analysis of linear feedback systems described by integral equations and with a time-varying (more specifically, periodic switching) feedback gain. In contrast to Lyapunov approaches widely used in the literature of switched systems, a non-Lyapunov framework is employed in this paper. The results obtained are in the frequency domain, which can be (i) applied to higher-order systems and (ii) easily verified based on the phase plot of the plant, which are illustrated by examples.