Condition of the elimination of overflow oscillations in two‐dimensional digital filters with external interference

Abstract

This study is concerned with the problem of the elimination of overflow oscillations (EOOs) for two-dimensional (2D) digital filters with external interference. The main purpose is the presentation of a new unified criterion such that the underlying 2D digital filter is stable with a positive prescribed interference attenuation level. A performance index is proposed for the first time, which is referred to as generalised dissipativity property. By using this index and two harmonic slack matrices, a novel criterion is established, which can be used to solve ℋ∞ EOOs, passive EOOs and l 2–l ∞ EOOs for 2D digital filters with external interference in a unified framework, and reduce the conservatism of the existing results. The effectiveness of the criterion is demonstrated by a numerical example.