Discretisation of Feeback Controllers in a Pointwise Gap Metric

Submitted to the 39th IEEE Conference on Decision and Control, 2000.

Discretisation of Feedback Controllers in a Pointwise Gap Metric

Michael Cantoni and Glenn Vinnicombe

Abstract 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 nu-gap metric, from the original LTI controller. Importantly, discretisation according to the procedure proposed permits an explicit characterisation of possible degradation in closed-loop performance (accounting for stability and inter-sample behaviour.) The main result demonstrates 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.