On the characterization of sampled-data controllers in the lifted domain

In this paper, we address sampled-data control problems on which the sampling and hold devices are not fixed beforehand, but are chosen as part of the design process. The idea is to apply the lifting transformation to the plant and then characterize the set of generalized sampled-data controllers, i.e., those that can be implemented as the cascade of a generalized sampler, a discrete-time controller and a generalized hold. We argue that our approach offers significant advantages over previous works, and will illustrate this by considering three applications: the input/output stabilization by generalized sampled-data controllers, the solution of the H-infinity optimal control problem and the combination of analog and digital controllers.