Asymptotic properties of the best sampled-data control performance

Properties of the best achievable performance of sampled-data control syste ms are investigated in this note. Contrary to our intuition, the best sampl ed-data control performance does not always converge to the best continuous -time control performance, even as the sampling period approaches zero. A c ounterexample is presented and a lifting-based analysis is performed, It is shown that the performance convergence is guaranteed if, and only if, a ce rtain Hankel norm and an aliasing effect computed from a specified antialia sing filter tend to vanish with a decreasing sampling period. It is also sh own that this condition is reduced to a simpler form if the specified filte r has special forms, These results can be generalized to a system involving a generalized hold.