State-space family realization of 2-D linear digital systems

A procedure is proposed for obtaining a family of state-space models from a two-dimensional transfer function matrix. The resulting model is in terms of an arbitrary parameter a. By substituting different values of a, different realizations with the same transfer function matrix are obtained. The proposed technique utilizes the method given by R. Eising (IEEE Trans. Automat. Control, vol.AC-23, p.793-9, 1978), and the final state-space model is in the form of R.P. Roesser´s (1975) 2-D model. Two different levels of family realization are obtained by expansion of the transfer function matrix about the arbitrary parameter a. The resulting system matrices from the family realisation algorithm are more general than the system matrices obtained from existing algorithms and should be useful in those applications where a secondary criterion can be optimized by varying an arbitrary parameter a. The procedure is illustrated with the help of an example