Rocha, P.; Willems, J. C. State for 2-D systems. (English) Zbl 0679.93002 Linear Algebra Appl. 122-124, 1003-1038 (1989). Summary: A new definition of state for N-D systems is given in a noncausal context. This definition is based on a deterministic Markovian-like property. It is shown that, for the particular case of (AR) 2-D systems, it yields systems that can be described by a special kind of first-order equations. The solutions of these equations can be simulated by means of a local line-by-line computational scheme. Cited in 12 Documents MSC: 93A10 General systems 93B25 Algebraic methods Keywords:N-D systems; deterministic Markovian-like property PDF BibTeX XML Full Text: DOI References:  Attasi, S., Systèmes linéaires homogènes à deux indices, INRIA rapport de recherche, (1973), No. 31 · Zbl 0278.65124  Fornasini, E.; Marchesini, G., State space realization theory of two-dimensional filters, IEEE trans. automat. control, AC-21, 4, 484-492, (1976) · Zbl 0332.93072  Gantmacher, F.R., The theory of matrices, Vol. II, (1960), Chelsea · Zbl 0088.25103  Roesser, R.P., A discrete state space model for linear image processing, IEEE trans. automat. control, AC-20, 1, 1-10, (1975) · Zbl 0304.68099  Willems, J.C., From time series to linear system—part I, Automatica, 22, 5, 561-580, (1986) · Zbl 0604.62090  Willems, J.C., Models for dynamics, Dynamics reported, 2, 171-269, (1989)  Woods, J., Two-dimensional discrete Markovian fields, IEEE trans. inform. theory, IT-18, 2, 232-240, (1972) · Zbl 0235.60063  Zariski, O.; Samuel, P., Commutative algebra, (1958), Van Nostrand Reinhold New York · Zbl 0121.27801 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.