New results on saturation overflow stability of 2-D state-space digital filters described by the Fornasini–Marchesini second model

• New saturation overflow stability criterion for 2-D digital filters is proposed.
• Criterion is based on a novel characterization of saturation nonlinearities.
• Criterion is less stringent than several existing criteria.

In this paper, the problem of global asymptotic stability of two-dimensional fixed-point state-space digital filters described by the Fornasini–Marchesini second local state-space model with saturation nonlinearities has been investigated. By making use of a precise upper bound of the system state vector and a novel passivity property associated with the saturation nonlinearities, a new sufficient global asymptotic stability criterion has been proposed. Presented criterion has been compared with several existing criteria. An illustrative example is given to demonstrate the efficacy of the proposed method.