Robust Controller Synthesis for the Attenuation of Non-Stationary Sinusoidal Disturbances with Uncertain Frequencies

Attenuation of sinusoidal disturbances with uncertain and arbitrarily time-varying frequencies is considered. The disturbances are modeled as the outputs of an autonomous exogenous system, whose system matrix depends on some uncertain parameters and is yet skewsymmetric for all admissible parameter values. A procedure is then developed for the synthesis of a linear time-invariant controller that guarantees a desired level of attenuation at steady-state as well as sufficiently fast transient response in the face of all admissible parameter variations. The procedure is based on solving a convex optimization problem in which the variables are subject to a set of linear matrix inequality as well as equality constraints. The order of the controller is equal to the order of the plant plus the order of the exogenous system.