AN EFFICIENT METHOD FOR THE EVALUATION OF THE CONTROLLABILITY AND OBSERVABILITY GRAMIANS OF 2-D DIGITAL-FILTERS AND SYSTEMS

An efficient and general method for the evaluation of the gramians of causal, stable, 2-D 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 2-D gramians with respect to accuracy and computational efficiency. The results obtained show that the new method leads to an accurate evaluation of the 2-D gramians and, furthermore, it requires only a small fraction of the computation required by existing methods.