An improved closed-loop stability related measure for finite-precision digital controller realizations

The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller implemented with finite word length (FWL), is used. A stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure.