The best achievable performance of sampled-data control systems with a small sampling period

This report shows that the best achievable performance of sampled-data control systems does not necessarily converge to that of continuous-time control systems even if a sampling period approaches zero. Moreover, it studies when a sampled-data system has the converging property and when it does not. Especially, a necessary and sufficient condition in order to guarantee convergence for almost all plants is obtained. The present analysis uses a lifting-based framework for sampled-data systems, which can treat a large class of generalized samplers and holds