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, it has previously been shown, 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 non-linear state feedback. In this paper the authors 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