Robust control for uncertain linear systems with sinusoidal disturbance of uncertain frequencies

The paper presents an output feedback controller design method for uncertain linear systems with sinusoidal disturbance of uncertain frequencies. The controller needs to compensate for the deterioration in performance due to the uncertain frequencies of sinusoidal disturbance. To this end, the authors introduce a virtual system which includes dynamics corresponding to uncertain frequencies, and design a controller which minimises the output difference between the virtual system and the closed-loop system. In other words, the controller is designed so that the closed-loop system approximates to the virtual system. The feedback controller is achieved by solving an LMI optimisation problem involving a robust H^∞ constraint. The proposed design method is illustrated using the track-following system of an optical disk drive. The advantages of the proposed design method are examined by comparing it with a design method that only minimises the H^∞ norm of the transfer function between sinusoidal disturbance and output