Presented at the 37th IEEE Conference on Decision and Control, 1998.

This paper is concerned with the development of quantitative results that lead to a characterisation of the uncertainty types to which linear, periodically-time-varying (LPTV), closed-loop systems are insensitive. The results are expressed in terms of the gap metric, which is a measure of the distance between the graphs of two systems. Towards establishing the main results, a formula for the directed gap if derived for LPTV systems. This formula is essentially a generalisation of that given in \cite{georgiou}, for linear, time-invariant (LTI) systems. In fact, all of the results obtained in this paper are analogous to those known to hold for LTI systems \cite{gs90,sefton} (although they do not follow directly from these). Importantly, the results presented in this paper apply to a class of sampled-data (SD) control-systems as a special case and are a step towards characterising the quality of SD approximations of LTI, continuous-time controllers.

Key Words: Periodically Time-Varying, Gap-Metric Robustness, Sampled-Data.