Hankel Norm Performance of Digital Filters Associated with Saturation

This brief proposes a new approach to the examination and reduction of the undesired memory effect of digital filters joined with saturation, which is known as system ringing. A new criterion is established to ascertain the Hankel norm performance of digital filters joined with saturation. Using this criterion, it is possible to check the reduction of undesired responses of the filters to past excitations. The asymptotic stability for the digital filters is ensured without external input under the proposed criterion. Three improved criteria for the Hankel norm performance of digital filters are also presented based on the diagonally dominant matrix approach. A numerical simulation shows the usefulness of the developed method.