Nonlinear control for robust rejection of periodic disturbances

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.