Realization of two's complement overflow limit cycle free state-space digital filters: A frequency-domain viewpoint

The "state-space" criterion (namely,
D- A^{T} DA > O, D
a positive diagonal matrix) due to Mills, Mullis, and Roberts [1] for the absence of overflow oscillations in state-space digital filters designed with two's complement arithmetic is well-known [2]-[4]. A frequency-domain formulation of this criterion is presented herein. It is shown that the criterion in this frequency form was implicity known in the literature prior to the appearance of the state-space criterion.