New Results in 2-D Systems Theory, Part II: 2-D State-Space Models—Realization and the Notions of Controllability, Observability, and Minimality

Proceedings of the IEEE

Volumn 65, Issue 6, 1977, Pages 945-961

  Kung, Sun Yuan ^a   Lévy, Bernard C ^a   Morf, Martin ^a   Kailath, Thomas ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

2-D SYSTEMS THEORY; MINIMALITY; OBSERVABILITY;

CONTROL SYSTEMS - CONTROLLABILITY; ELECTRIC FILTERS, DIGITAL; MATHEMATICAL MODELS; MATHEMATICAL TECHNIQUES - STATE SPACE METHODS;

SYSTEMS SCIENCE AND CYBERNETICS;

EID: 0017500725     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1977.10592     Document Type: Article

References (17)

1. S. Attasi, “Systemes lineaires homogènes à deux indices,” Rapport Laboria, no. 31, Sept. 1973.
2. —, “Modélisation et traitement des suites à deux indices,” Rapport Laboria, Sept. 1975.
3. E. Fornasini and G. Marchesini, “Algebraic realization theory of two-dimensional filters,” in Variable Structure Systems, A. Ruberti and R. Mohler, Eds. New York: Springer Verlag (Springer Lecture Notes in Economics and Mathematical Systems), 1975.
4. —, “State-space realization theory of two-dimensional filters,” IEEE Trans. Automat Contr., vol. AC-21, pp. 484–492, Aug. 1976.
5. D. D. Givone and R. P. Roesser, “Minimization of multidimensional linear iterative circuits,” IEEE Trans. Comput., vol. C-22, pp. 673–678, July 1973.
6. W. A. Wolovich, Linear Multivariable Systems. New York: Springer-Verlag, 1974.
7. R. E. Mullans and D. L. Elliott, “Linear systems on partially ordered time sets,” in Proc. 1973 IEEE Conf. Decision and Control, pp. 334–337, 1973.
8. D. D. Givone and R. P. Roesser, “Multidimensional linear iterative circuits—general properties,” IEEE Trans. Comput., vol. C-21, pp. 1067–1073, Oct. 1972.
9. S. K. Mitra, A. D. Sagar, and N. A. Pendergrass, “Realizations of two-dimensional recursive digital filters,” IEEE Trans. Circuits and Systems, vol. CAS-22, pp. 177–184, Mar. 1975.
10. V. Zakian and N. S. Williams, “Canonical state equations of delay differential systems,” Control Systems Centre, Rep. 213, Univ. Manchester, Manchester, England, July 1973.
11. C. T. Chen, Introduction to Linear System Theory. New York: Holt, Rinehart and Winston, 1970.
12. R. R. Read, J. L. Shanks, and S. Treitel, “Two-dimensional recursive filtering,” in Topics in Applied Physics. New York: Springer-Verlag, 1975, vol. 6, pp. 137–176.
13. R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Trans. Automat. Contr., vol. AC-20, pp. 1–10, Feb. 1975.
14. B. Vilfan, “Another proof of the two-dimensional Cayley-Hamilton theorem,” IEEE Trans. Comput., vol. C-22, p. 1140, Dec. 1973.
15. R. E. Kaiman, P. Falb, and M. Arbib, Topics in Mathematical System Theory. New York: McGraw-Hill (International Series in Pure and Applied Mathematics), 1969.
16. H. H. Rosenbrock, State Space and Multivariable Theory. New York: Wiley, 1970.
17. S. Y. Kung, “An easy method for inverse system realizations and its applications,” to be submitted.