Worst case l∞ to l∞ gain minimization: dynamic versus static state feedback

It has been recently shown that for the problem of optimal rejection of persistent disturbances using full-state feedback, static nonlinear controllers can recover the performance level achieved by any linear dynamic controller. In this paper we complement these results by showing that for this problem nonlinear dynamic time-varying finite dimensional, possibly discontinuous, compensators do not offer any advantage over memoryless time invariant nonlinear-compensators. Moreover, we show that the best possible (over the set of all stabilizing controllers) disturbance rejection can be achieved by using globally Lipschitz piecewise-linear controllers