Adaptive stabilization of linear systems with outputs affected by unknown sinusoidal disturbances

Known linear stabilizable and detectable systems are considered when the measured output is affected by sinusoidal disturbances generated by an unknown exosystem. The output feedback stabilization problem is addressed: necessary and sufficient conditions for the solution of the problem are given. An adaptive control strategy is described that provides, via adaptive observer techniques, suitable estimates of the extended system state variables which are then used for exponential stabilization. An example with a disturbance containing two unknown frequencies is worked out in detail and simulated.