A state-space realization form of two-dimensional transfer functions

In this paper, we propose a method for obtaining the state-space realization form of two-dimensional transfer functions (2DTF). By using our method, realization form can be directly obtained from the coefficients of the 2DTF, without performing canonical decomposition of the state equations and solving nonlinear equations. Consider the possibility of reducing the realization dimension in our state-space realization form, and obtain conditions imposed on 2DTF for the reduction. Moreover, we present a class of 2DTF that can be realized with a minimal dimension with respect to both of two variables.