Low order nonlinear controllers for the rejection of persistent bounded disturbances

The l₁-optimal linear time-invariant (LTI) compensator may have an order significantly higher than that of the plant. Here the authors consider the square discrete time multivariable setting in which T₃^-1 is stable, and show, under a technical assumption, that there always exists a low order nonlinear stabilizing controller which provides the same level of performance as a given LTI stabilizing controller. Furthermore, for the scalar case the authors present an algorithm which can be used to compute the optimal performance which can be achieved by a nonlinear time-varying stabilizing controller