Persistent disturbance rejection via static-state feedback

In contrast with ℋ_∞ and ℋ₂ control theories, the problem of persistent disturbance rejection (l¹ optimal control) leads to dynamic controllers, even when the states of the plant are available for feedback. Using viability theory, Shamma showed (1993), in a nonconstructive way, 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 l¹ norm achieved by any stabilizing state-feedback linear dynamic controller can be also achieved using a memoryless variable structure controller