A note on asymptotic stabilization of linear systems by periodic, piecewise constant, output feedback

Abstract

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.