Multi-sinusoidal disturbance rejection for discrete-time uncertain stable systems

Linear single-input single-output discrete-time systems P(z) with unknown parameters, order and relative degree are considered, which are perturbed by biased sinusoidal disturbances. Under the assumption that the disturbance frequencies, the sign of the static gain P(1), the sign of either Re[P(ejωi)] or Im[P(ejωi)], for any disturbance frequency ωi, are known, linear disturbance compensators are proposed which achieve exponential disturbance suppression. Such results are then locally extended to the case of disturbances with unknown frequencies.