Stability analysis of two-dimensional digital recursive filters

A new approach to the stability problem for the two-dimensional digital recursive filter is presented. The bivariate difference equation representation of the two-dimensional recursive digital filter Is converted to a multiinput-muliloutput (MIMO) system similar to the statespace representation of the one-dimensional digital recursive filter. In this paper, a pseudo-state representation is used and three coefficient matrices are obtained. A general theorem for stability of two-dimensional digital recursive filters is derived and a very useful theorem is presented which expresses sufficient requirements for instability in terms of the spectral radii of these matrices.