Control over bandlimited communication channels: limitations to stabilizability

This paper concerns the sampled data control of continuous time plants from a remote location when the feedback and actuation signals are transmitted over finite bandwidth communication channels. We show two results. First that under the theoretical restriction of perfect bandlimitation an unstable plant cannot be stabilized, if the actuation and feedback data are transmitted at rates exceeding the Nyquist frequencies of the communications channels. Under more practical bandlimitations, we show that super-Nyquist rates result in closed loop H_∞ norms that grow with the severity with which band confinement is imposed. In theory these problems do not appear if sub-Nyquist rates are used. We explain in the paper that this loss of Stabilizability is a consequence of a fundamental interplay between communications and control.