An efficient method for the evaluation of the controllability and observability Gramians of 2D digital filters and systems

An efficient and general method for the evaluation of the Gramians of causal, stable, 2D recursive digital filters and systems is proposed. The method is based on a two-stage extension of the Astrom-Jury-Agniel algorithm which was originally used for the evaluation of the scalar loss function of a stationary random process with rational spectral density. The new method is compared with other known methods for the evaluation of 2D Gramians with respect to accuracy and computational efficiency. The results obtained show that the new method leads to an accurate evaluation of the 2D Gramians and, furthermore, it requires only a small fraction of the computation required by existing methods