Balanced realization and model reduction of 3-D separable-denominator transfer functions (Q1101383)

After showing a necessary and sufficient condition to be separately locally controllable and separately locally observable, controllability and observability Gramians are introduced for a three-dimensional (3-D) separable-denominator state-space model. A technique is then developed for realizing a 3-D minimal state-space model in balanced form from a given 3-D rational transfer function with separable denominator. This technique is applicable to the model reduction of 3-D separable- denominator digital filters.