Finite precision digital system structures with stability and roundoff noise considerations

The stability behavior and the error propagation of a digital system implemented with finite word length are investigated. Based on a first-order approximation, a stability robustness related measure is derived. This measure is shown to be dependent on the structures or realizations of the system. The optimal structures are defined as those that maximize this measure, and a class of solutions is given. Roundoff noise is minimized subject to maximizing the derived stability measure. Two numerical examples are presented to show the design procedure