Dynamic stabilising controllers for linear time-invariant systems and multirate control

Abstract

For a given linear time-invariant plant-compensator pair in a closed-loop, it is shown that, if a simple matrix equation holds, the closed-loop system behaves like a functional observer of a linear function of the state of the plant. If such a function can be used to augment the plant output, it is possible to use a static output feedback from the augmented output, thus obtaining as a closed-loop system the restriction of the original one to a suitable invariant subspace. A dual result holds too, ensuring stabilisation by static output feedback with an augmented input. If the plant output/input cannot be augmented, the use of multirate samplers/holders is proposed in order to equivalently augment the outputs or inputs of the controlled plant, 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 stabilise the plant.