On disturbance attenuation for linear systems under stable, additive plant perturbations

This paper deals with linear systems and the disturbance attenuation problem of minimizing a given operatorial norm of the lower linear fractional transformation between a generalized plant and a controller. We show that the optimal gain attainable by causal feedback does not depend on linear, stable, additive plant perturbations, irrespective of the chosen norm. The result proves applicable to an important class of decentralized control configurations. Applications to reducing the computational effort for the optimal controller synthesis are also discussed.