$l_{2} - l_{\infty}$ Elimination of Overflow Oscillations in 2-D Digital Filters Described by Roesser Model With External Interference

Abstract

Two-dimensional (2-D) digital filters can be corrupted by external interferences, but no stability criteria have yet been established. This brief proposes a new <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> stability criterion for the absence of limit cycles in 2-D digital filters that are described by Roesser model with external interference. Our new criterion ensures the attenuation of the effect of external interference on 2-D digital filters to a prescribed level. This criterion also guarantees the asymptotic stability result without external interference. The proposed criterion is represented in terms of linear matrix inequality, which can be verified by using existing numerical packages. We use an illustrative example to demonstrate the effectiveness of the proposed criterion.