A multirate approach to input or output augmentation for sampled-data static output feedback

As pointed out in [S. Galeani, et al., 2003], provided a simple matrix equation holds for a given plant-compensator pair in closed-loop, the closed-loop system behaves like a functional observer of a linear function of the state of the plant. As a consequence, if the plant output can be augmented by such a function, a static output feedback from the augmented output stabilizes the controlled system. Similarly, if a dual equation holds, a static output feedback stabilizes the controlled system with a suitably augmented input. In this paper the use of multirate samplers/holders to equivalently augment the outputs or inputs of the controlled plant is shown, thus making the technique suitable even if no additional sensors/actuators can be placed on the plant. The proposed multirate controllers are either static or asymptotically stable, and thus strongly stabilizing.