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 before-hand, 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_∞ optimal control problem and the combination of analog and digital controllers.