Model reduction of two-dimensional discrete systems

In this paper the one-dimensional (1-D) reduction method of Badreddin-Mansour is extended to two-dimensional (2-D) discrete systems. It is found by counterexample that contrary to the 1-D case, stability is not guaranteed, for the reduced model, in general. However, stability is guaranteed for the reduced model if the original system is stable, in the following two cases: (1) the original system is of the separable type; and/or (2) the original system is of dimension one in each of the horizontally and vertically propagation sections, i.e., a lh-lv system. Several examples are given to illustrate the reduction procedure, and its effect on stability.