Zerz, Eva Primeness of multivariate polynomial matrices. (English) Zbl 0866.93053 Syst. Control Lett. 29, No. 3, 139-145 (1996). Summary: Different characterizations of primeness of polynomial matrices that are mutually equivalent in the one-dimensional case of univariate polynomials lead to various primeness concepts in the multivariate situation. Applied to systems theory, this fact gives rise to a more refined view to observability and controllability of multidimensional systems. Algorithms for testing primeness properties are given based on computer algebraic techniques. Cited in 23 Documents MSC: 93C35 Multivariable systems, multidimensional control systems 93B05 Controllability 93C05 Linear systems in control theory 12D05 Polynomials in real and complex fields: factorization Keywords:Gröbner bases; observability; controllability; multidimensional systems; primeness PDFBibTeX XMLCite \textit{E. Zerz}, Syst. Control Lett. 29, No. 3, 139--145 (1996; Zbl 0866.93053) Full Text: DOI References: [1] Becker, T.; Weispfenning, V., Gröbner Bases, (Graduate Texts in Mathematics, Vol. 141 (1993), Springer: Springer New York) [2] Bose, N. K., Applied Multidimensional Systems Theory (1982), Van Nostrand Reinhold: Van Nostrand Reinhold New York · Zbl 0574.93031 [3] Buchberger, B., Grobner bases: an algorithmic method in polynomial ideal theory, (Bose, N. K., Multidimensional Systems Theory (1985), Reidel: Reidel Dordrecht), 184-232 · Zbl 0587.13009 [4] Morf, M.; Levy, B. C.; Kung, S. Y., New results in 2-D systems theory, Part I: 2-D polynomial matrices, factorization, and coprimeness, (Proc. IEEE, 65 (1977)), 861-872 [5] Oberst, U., Multidimensional constant linear systems, Acta Appl. Math., 20, 1-175 (1990) · Zbl 0715.93014 [6] Rocha, P., Structure and representation of 2-D systems, (Ph.D. Thesis (1990), University of Groningen) [7] Rocha, P.; Willems, J. C., Controllability of 2-D systems, IEEE Trans. Automat. Control, 36, 413-423 (1991) · Zbl 0753.93008 [8] Rocha, P.; Willems, J. C., On the representation of 2-D systems, Kybernetika, 27, 225-230 (1991) · Zbl 0746.93016 [9] Rosenbrock, H. H., State-space and Multivariable Theory (1970), Nelson: Nelson London · Zbl 0246.93010 [10] Willems, J. C., Paradigms and puzzles in the theory of dynamical systems, IEEE Trans. Automat. Control, 36, 259-294 (1991) · Zbl 0737.93004 [11] Youla, D. C.; Gnavi, G., Notes on n-dimensional system theory, IEEE Trans. Circuits Systems, 26, 105-111 (1979) · Zbl 0394.93004 [12] Zerz, E., The canonical Cauchy problem for linear systems of partial difference equations over the complete integral lattice, (Ph.D. Thesis (1994), University of Innsbruck) [13] E. Zerz, Primeness notions for multivariate polynomial matrices, Proc. 35th IEEE Conf on Decision and Control; E. Zerz, Primeness notions for multivariate polynomial matrices, Proc. 35th IEEE Conf on Decision and Control · Zbl 0866.93053 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.