Hyperstability and adaptive filtering

Recently, results from the area of system identification concerning the concept of system hyperstability have been applied to the analysis of adaptive filtering configurations. In particular, this analysis tool has allowed the development of a family of convergent adaptive recursive digital filtering algorithms, where the use of conventional gradient analysis techniques had proven insufficient. This correspondence provides a somewhat informal explanation of hyperstability analysis as might be useful to the adaptive signal processing community, and clarifies its implications and limitations.