Balanced realization and model reduction of 2-D discrete systems with variable coefficients

A two-dimensional (2-D) model with variable coefficients is introduced, and a technique for 2-D model reduction is presented. It is shown that the stability of the reduced model is guaranteed for a class of 2-D systems with variable coefficients. It is also shown that, once a balancing structure is determined, the relative size of diagonal entries of the horizontal and vertical Grammian matrices can be used to extract a suitable subsystem which represents a reduced-order model for the original one