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Nonlinear Control for Robust Rejection of Periodic Disturbances

## R.C.H. Lee and M.C. Smith

## Abstract

Consider a linear plant with a strictly proper rational transfer
function and an input which is a known periodic waveform of unknown
amplitude and phase. In the case when the periodic waveform has
infinitely many non-zero harmonics, it is pointed out that for a wide
class of linear , time-invariant (infinite-dimensional)
controllers, it is not possible to robustly stabilize the plant and
achieve asymptotic rejection of the disturbance. For a specific
linear plant and a triangular wave disturbance, it is shown by
construction that the problem is soluble with a nonlinear
controller. Robustness is measured using the gap metric robust
stability margin.