Robust generalized asymptotic regulation via an LPV controller without parameter derivative dependence

Attenuation of sinusoidal disturbances with uncertain and arbitrarily time-varying frequencies is considered for a plant that depends on online measurable parameters. The disturbances are modeled as the outputs of a neutrally stable exogenous system that depends on measurable as well as unmeasurable parameters. Solvability conditions are then derived in the form of parameter-dependent matrix inequalities, based on which a linear parameter-varying controller synthesis procedure is outlined. Alternative conditions are provided for the synthesis of a controller that has no dependence on the derivatives of the parameters. It is also clarified how the transient behavior of the controller can be improved.