2-D weighted impulse response Gramians and model reduction of 2-D separable denominator digital systems

The weighted impulse response Gramians of two-dimensional (2-D) separable denominator digital systems are defined based on the definition proposed by Sreeram and Agathoklis (1991, 1993) for the 1-D case. These Gramians are then applied to present a model reduction method for such 2-D systems. The reduced-order system is always stable if the original 2-D system is stable. A numerical example is illustrated and compared with well known 2-D model reduction method