In contrast with /spl Hscr//sub /spl infin// and /spl Hscr//sub 2/ control theories, the problem of persistent disturbance rejection (l/sup 1/ 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 l/sup 1/ norm achieved by any stabilizing state-feedback linear dynamic controller can be also achieved using a memoryless variable structure controller.
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