Comparing digital implementation via the bilinear and step-invariant transformations

摘要

From an analog system K, digital systems K{sub}d and K{sub}(bt) are often obtained via the step-invariant and bilinear transformations, respectively. For the case when K is stable, it is shown that under certain conditions, K{sub}(bt) converges to K{sub}d in l{sub}p induced norms as the sampling period tends to zero for 1 ≤ p ≤ ∞. Furthermore, K{sub}(bt) converges to K{sub}d in the graph metric as the sampling period tends to zero no matter whether K is stable or not.