Abstract. For a controllable linear time-invariant system x = Ax+bu(t) in R n a general delayed feedback action u(t) = −k(t)u(t − τ) is proposed so that the solutions of the closed-loop system x = Ax − bk(t)x(t − τ) are driven to zero in finite time. Optimality with respect to some integral performance indices is also analyzed.Mathematics subject classification (2010): 35R10, 35R35, 35K20.