Computation and convergence of frequency response via fast sampling for sampled-data control systems

This paper proves that the frequency responses of fast-sample/fast-hold approximations of a sampled-data system converge to that of the original system as the sampling rate gets faster. While this may appear to hold trivially, there is a serious technical difficulty, and the proof is indeed nontrivial. It is also guaranteed that this convergence is uniform on the total frequency range. A numerical example is given to illustrate the result