Discretisation of feedback controllers in a pointwise gap metric

In this paper, a new technique for discretising linear time-invariant (LTI) feedback controllers is proposed. The resulting sampled-data (SD) approximation is guaranteed to lie within a pointwise gap distance, closely related to the v-gap metric, from the original LTI controller. Importantly, this permits explicit characterisation of possible degradation in closed-loop performance (accounting for stability and inter-sample behaviour.) It is shown that SD approximation, to within a bound on the pointwise gap metric defined, can be posed as a standard H-infinity SD synthesis problem, which may be solved via existing methods.