Intersample and finite wordlength effects in sampled-data problems

We consider the behaviour of digital control systems from the point of view of modeling intersample behavior, and the effects of quantizations and finite wordlength computations. Our purpose in this paper is to investigate the dependence of these two effects on the sampling rate. We show that there is essentially a tradeoff between guarding against these two effects, in that fast sampling will generally improve intersample behavior, while it makes the system more sensitive to finite arithmetic effects. We develop quantitative measures for performance under these two combined effects using input-output norms. We address the problem of intersample behavior using the by now well known lifting technique, while we investigate roundoff error effects by modeling them as feedback with certain types of switching nonlinearities. We present examples that exhibit these tradeoffs.