Stability analysis of 2-D digital filters described by the Fornasini-Marchesini second model using overflow nonlinearities

This paper discusses new criteria for the global asymptotic stability of two-dimensional (2-D) digital tilters described by the Fornasini-Marchesini second local state-space model subject to overflow nonlinearities. For saturation and triangular arithmetics, the presented approach will always lead to a larger overflow stability region in the parameter-space, as compared to a recent criterion due to Liu; for other overflow nonlinearities, new criteria may generally provide results as supplement to those obtainable from Liu's criterion. The approach leads to a more relaxed saturation overflow stability condition, as compared to a recent criterion due to Hinamoto. Finally, the approach is extended to the situations involving quantization nonlinearities.