Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency

Asymptotically stable, observable linear systems of order n which are not required to be minimum phase and are affected by an additive noisy biased sinusoidal disturbance with unknown bias, magnitude, phase and frequency are considered. The problem of designing an output feedback compensator which regulates the output to zero for any initial condition and for any biased sinusoidal disturbance with no noise is addressed, under the assumption that the system parameters are known. This problem is solved by a (2n+6)-order compensator which generates asymptotically convergent estimates of the biased sinusoidal disturbance and of its parameters, including frequency. The robustness of the closed loop system with respect to sufficiently small additive unmodelled noise is characterized in terms of input-to-state stability.