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

Abstract

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 skew-symmetric 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.