Comparison between continuous and discrete-time model truncation

The continuous and discrete-time balanced truncation (BT) and balanced stochastic truncation (BST) model reduction methods and their error bounds are reviewed. The investigation of the differences between the continuous and discrete-time model reduction methods yields a one-step-at-a-time discrete-time BT method, a one-step-at-a-time discrete-time BST method, and an important new relative-error bound for continuous-time BST. The new relative-error bound differs from previous results in that the error is relative to the truncated model rather than the original model. Three other results come out from the analysis: (i) algorithms for discrete-time BST, (ii) error bound comparisons, and (ii) transformations between different power spectrum factorizations. The formulas and the properties of bilinear transformations used in the comparison analysis are provided