Absence on Extreme-point Results in Sampled Data Control Systems

Abstract

This paper considers the robustness of sampled-data control systems when the continuous-time open loop system has parametric uncertainty having either an interval or affine structure. For these cases we show that no extreme point results exist and indicate the difficulties one encounters in extending the Edge Theorem to such sampled-data control systems. Presently, the existence of an edge result for sampled-data control systems is an open question with the only positive result occuring for the case of sufficiently small sampling period.