Multidimensional state-space models: A comparative overview

This paper provides a comparative survey of the existing multidimensional state-space models. The 2-Dimensional state-space models are first presented and compared to each other from both the mathematical and the applications point of view. Then a canonical 3-Dimensional state space realization is considered and its applications are briefly discussed. Finally the special cases of 2-D and 3-D first-order transfer functions are investigated and necessary and sufficient conditions for existence of respective minimal state-space realizations are introduced. The models considered in the paper have been used for treating various design problems of multidimensional systems such as model mathing, transfer function separation, etc., as can be seen in the corresponding references.