Abstract
New sufficient conditions for minimal realization of 2-D systems are given. Based on these, a method of minimization of the dimension of a realization is proposed and illustrated by examples. Finally the question of the existence of a minimal realization is discussed.
Research supported by the National Science Foundation under Grant No. ECS 82 17375
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
N. K. Bose, Applied Multidimensional Systems Theory, Van Nostrand Reinhold Company, New York, 1982.
B. C. Lévy, 2-D polynomial and rational matrices, and their applications for the modeling of 2-D dynamical systems, Technical Report No. M735-11, Stanford University, June 1981.
E. D. Sontag, On first-order equations for multidimensional filters, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-26, No. 5, pp. 480–482, 1978.
R. Eising, Realization and stabilization of 2-D systems, IEEE Trans. Automat. Cont., vol. AC-23, No. 5, pp. 793–799, 1978.
R. E. Kalman, Irreducible realizations and the degree of a rational matrix, J. Soc. Indust. Appl. Math, vol. 13, No. 2, pp. 520–544, 1965.
T. Kailath, Linear Systems, Englewood Cliffs, NJ. Prentice-Hall, 1980.
M. Morf, B. C. Lévy, and S-Y. Kung, New results in 2-D systems theory, Part I: 2-D polynomial matrices, factorization, and coprimeness, Proc. IEEE, vol. 65, pp. 861–872, 1977.
S-Y. Kung, B. C. Lévy, M. Morf and T. Kailath, New results in 2-D systems theory, Part II: 2-D state-space models-realization and the notions of controllability, observability, and minimality, ibidem, pp. 945–961.
E. W. Kamen, Lectures on Algebraic System Theory: Linear Systems Over Rings, NASA Contractor Report 3016, 1978.
E. B. Lee, Linear hereditary control systems, in Calculus of Variations and Control Theory, Academic Press, Inc., pp. 47–72, 1976.
R. P. Roesser, A discrete state-space model for linear image processing, IEEE Trans. Automat. Cont., vol. AC-20, No. 1, pp. 1–10, 1975.
S. K. Mitra, A. D. Sagar, and N. A. Pendergrass, Realizations of two-dimensional recursive digital filters, IEEE Trans. Circuits Syst., vol. CAS-22, No. 3, pp. 177–184, 1975.
A. I. G. Vardulakis, D. N. J. Limebeer and N. Karcanias, Structure and Smith-McMillan form of a rational matrix at infinity, Int. J. Control, vol. 35, No. 4, pp. 701–725, 1982.
A. I. G. Vardulakis and N. Karcanias, Proper, minimal McMillan degree bases of rational vector spaces, Technical Report CUED/F-CAMS/TR-226, Cambridge University, Engineering Department, 1981.
G. C. Verghese, B. C. Levy and T. Kailath, A generalized state-space for singular systems, IEEE Trans. Automat. Cont., vol. AC-26, No. 4, pp. 811–831, 1981.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Bruce Lee, E., Zak, S.H. (1984). Remarks on minimal realizations of 2-D systems. In: Fuhrmann, P.A. (eds) Mathematical Theory of Networks and Systems. Lecture Notes in Control and Information Sciences, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031088
Download citation
DOI: https://doi.org/10.1007/BFb0031088
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13168-7
Online ISBN: 978-3-540-38826-5
eBook Packages: Springer Book Archive