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

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 l₂-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.