This note studies the asymptotic stabilization problem for controllable and observable, single-input single-output, linear, time-invariant, continuous-time systems by means of memoryless output feedback of the form u(t) = k(t)y(t), with k(t) periodic and piecewise constant. A necessary and sufficient condition, together with a simpler to test sufficient condition, given in terms of a bilinear matrix inequality, is presented. A few illustrative examples complete the paper. (C) 2004 Elsevier Ltd. All rights reserved.