On elimination of overflow oscillations in linear time-varying 2-D digital filters represented by a Roesser model

• Overflow elimination analysis for time-varying 2-D digital filters of Roesser type.
• Inaugural treatment of LPV approach for stability analysis of 2-D digital filters.
• Robust stability criterion is developed for dealing with external interferences.
• External interferences are considered both in state and output equations.
• Numerical example is provided for a 2-D filter with three parametric variations performance condition, for dealing with the external interferences.

This paper proposes a novel linear matrix inequality (LMI)-based stability criterion to avoid overflow oscillations in 2-D digital filters described by a Roesser state-space model with saturation-type overflow characteristics. In contrast to the conventional approaches, the proposed overflow oscillation elimination methodology can be applied to linear parameter varying time-variant digital filters under overflow subject to both state and output disturbances. For such filters, the proposed criterion ensures the zero-input overflow stability as well as robustness against interferences with a guaranteed H∞H∞ performance bound. A numerical example is presented to demonstrate the effectiveness of the proposed approach.