In contrast with H-infinity and H-2 control theories, the problem of persistent disturbance rejection (l(1) optimal control) leads to dynamic controllers, even when the states of the plant are available for feedback. Using viability theory, it has recently been shown, in a nonconstructive way [17], that in the state-feedback case the same performance achieved by any dynamic linear time-invariant controller can be achieved using memoryless nonlinear state feedback. In this paper we give an alternative, constructive proof of these results for discrete- and continuous-time systems. The main result of the paper shows that in both cases, the l(1) norm achieved by any stabilizing state feedback linear dynamic controller can be also achieved using a memoryless variable structure controller.