Abstract
This paper is concerned with some properties of transfer functions in two variables which can be realized by classes of 2D systems characterized by pairs of state updating matrices which generate algebras with special structures. Two situations are mainly considered. The first deals with pairs of matrices which generate a solvable Lie algebra (i.e. are simultaneously triangularizable). The second refers to pairs of matrices which generate abelian Lie algebras (i.e. the matrices commute).
The analysis of the connections between the properties of 2D realizations and transfer functions is based on the representation algorithms of non-commutative rational power series.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Fornasini E., and Marchesini G. (1978) "Doubly Indexed Dynamical Systems: State Space Models and Structural Properties", Mathematical Systems Theory, vol. 12, n. 1.
Fornasini E., and Marchesini G. (1976) "State Space Realization Theory of Two-Dimensional Filters", IEEE Trans on Automat. Contr., vol. AC-21, pp. 484–492.
Fornasini E., and Marchesini G. (1980) "On the Problem of Constructing Minimal Realizations for Two-Dimensional Filters", IEEE Trans PAMI, vol. 2, n. 2, pp. 172–76.
Attasi S. (1973) "Systèmes linéaries homogènes à deux indices", Rapport LABORIA, 31.
Bisiacco M., Fornasini E., and Marchesini G. (1983) "On Commutative Realizations of 2D Transfer Functions", Proc. of 1983 EES-MECO Congress, Athens.
Fornasini E., and Marchesini G. (1976) "Two Dimensional Filters: New Aspects of the Realization Theory", Third Int. Joint Conf. on Pattern Recognition, Coronado, California, Nov. 8–11.
Sontag E.D. (1978) "On First-Order Equations for Multi-Dimensional Filters", IEEE Trans ASSP, vol. 26, pp. 480–82.
Fliess M. (1974) "Matrices de Hankel", J. Math. Pures et Appl. 53, pp. 197–224.
McCoy N.H. (1936) "On the Characteristic Roots of Matric Polynomials", Bull. Amer. Math. Soc., pp. 592–600.
Motzkin T.S., Taussky O. (1952) "Pavis of Matrices with Property L", Trans Amer Math. Soc, vol. 73, pp. 108–114.
Suprunenko D.A., Tyshkevich R.I. (1968) "Commutative Matrices", Acad. Press..
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Fornasini, E., Marchesini, G. (1984). Some connections between algebraic properties of pairs of matrices and 2D systems realization. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 63. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006281
Download citation
DOI: https://doi.org/10.1007/BFb0006281
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13552-4
Online ISBN: 978-3-540-39010-7
eBook Packages: Springer Book Archive