Optimal damping of forced oscillations in periodically time-varying linear systems

This paper deals with a periodically time-varying linear system affected by external harmonic disturbances with known frequencies but unknown amplitudes. The problem is to construct a physically realizable optimal controller to damp the forced oscillations. It is shown that this type of controller does exist. It is universal optimal in the sense that it does not depend on the unknown amplitudes and is optimal for all choices of such parameters. It is robust with regard to the known frequencies in the sense that small deviation of the frequencies simply results in a small increase of the damping level of forced oscillations.