A time-suboptimal feedback control algorithm synthesis problem in linear non-stationary non-oscillatory systems is considered. The solution is obtained by a piecewise linear approximation of a time-optimal non-stationary switching surface and it has the formFδ(t,x)= sgn (pm(t)xx+ … +sgn P1(t)x +P1(t)xx)…) A method of calculation of row-vector parameters P1(l), P2(l).… PM(t)s developed.