A new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with interference

• A new criterion for H∞H∞ stability of 2-D digital filters in Fornasini–Marchesini second model is proposed.
• The effect of external interference on 2-D filters can be reduced to an attenuation level.
• The criterion guarantees asymptotic stability without external interference.
• The criterion is described by linear matrix inequality.

Stability criteria have been proposed previously by Ahn for two-dimensional (2-D) digital filters described by the Roesser model with external interference. However, no stability criteria have yet been established for 2-D digital filters described by the Fornasini–Marchesini second model. In this paper, we propose a new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with saturation arithmetic and external interference. This new criterion guarantees that 2-D digital filters in this model are asymptotically stable with a guaranteed H∞H∞ performance. The criterion is described by linear matrix inequalities (LMIs). Illustrative examples show the effectiveness of the proposed new criterion.