Output disturbance decoupling via disturbance-dependent state transformation

For a class of linear systems with external smooth disturbances, control design is considered to attenuate the effect of the disturbances on the outputs of the systems. To deal with the unmatched disturbances, a disturbance-dependent state transformation is introduced, so that the transformed disturbances satisfy the matching condition in the new state coordinates, and therefore we design controllers to compensate for the disturbances. The controller implementation is also considered. An simple example is given to demonstrate the design procedure and the effectiveness of the design.