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Journal of Control Science and Engineering
Volume 2012, Article ID 609276, 6 pages
http://dx.doi.org/10.1155/2012/609276
Research Article

Strict System Equivalence of 2D Linear Discrete State Space Models

Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khodh, 123 Muscat, Oman

Received 10 October 2011; Revised 30 January 2012; Accepted 6 February 2012

Academic Editor: L. Z. Yu

Copyright © 2012 Mohamed S. Boudellioua. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. H. Rosenbrock, State Space and Multivariable Theory, Nelson-Wiley, London, UK, 1970.
  2. P. A. Fuhrmann, “On strict system equivalence and similarity,” International Journal of Control, vol. 25, no. 1, pp. 5–10, 1977. View at Google Scholar · View at Scopus
  3. D.S. Johnson, Coprimeness in multidimensional system theory and symbolic computation, Ph.D. thesis, Loughborough University of Technology, Leicestershire, UK, 1993.
  4. A. C. Pugh, S. J. McInerney, M. Hou, and G. E. Hayton, “A transformation for 2-D systems and its invariants,” in Proceedings of the 35th IEEE Conference on Decision and Control, pp. 2157–2158, Kobe, Japan, December 1996. View at Scopus
  5. A. C. Pugh, S. J. McInerney, M. S. Boudellioua, D. S. Johnson, and G. E. Hayton, “A transformation for 2-D linear systems and a generalization of a theorem of Rosenbrock,” International Journal of Control, vol. 71, no. 3, pp. 491–503, 1998. View at Google Scholar · View at Scopus
  6. E. Zerz, “On strict system equivalence for multidimensional systems,” International Journal of Control, vol. 73, no. 6, pp. 495–504, 2000. View at Google Scholar · View at Scopus
  7. A. C. Pugh, S. J. McInerney, M. S. Boudellioua, and G. E. Hayton, “Matrix pencil equivalents of a general 2-D polynomial matrix,” International Journal of Control, vol. 71, no. 6, pp. 1027–1050, 1998. View at Google Scholar · View at Scopus
  8. A. C. Pugh, S. J. McInerney, and E. M. O. El-Nabrawy, “Equivalence and reduction of 2-D systems,” IEEE Transactions on Circuits and Systems II, vol. 52, no. 5, pp. 271–275, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. M. S. Boudellioua, “An equivalent matrix pencil for bivariate polynomial matrices,” International Journal of Applied Mathematics and Computer Science, vol. 16, no. 2, pp. 175–181, 2006. View at Google Scholar · View at Scopus
  10. M. S. Boudellioua, “On the simplification of systems of linear multidimensional equations,” in The Sage Days 24 Workshop on Symbolic Computation in Differential Algebra and Special Functions, Hagenberg, Austria, 2010. View at Google Scholar
  11. R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Transactions on Automatic Control, vol. 20, no. 1, pp. 1–10, 1975. View at Google Scholar · View at Scopus
  12. S. Attasi, “Systemes lineaires a deux indices,” Tech. Rep. 31, INRIA, Le Chesnay, France, 1973. View at Google Scholar
  13. E. Fornasini and G. Marchesini, “State space realization theory of twodimensional filters,” IEEE Transactions on Automatic Control, vol. 21, no. 4, pp. 484–492, 1976. View at Google Scholar · View at Scopus
  14. T. Kaczorek, “Singular models of 2-D systems,” in Proceedings of the 12th World Congress on Scientific Computation, Paris, France, 1988.
  15. E. Zerz, “Primeness of multivariate polynomial matrices,” Systems and Control Letters, vol. 29, no. 3, pp. 139–145, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. E. Zerz, Topics in Multidimensional Linear Systems Theory, Springer, London, UK, 2000.
  17. A. C. Pugh, S. J. McInerney, and E. M. O. El-Nabrawy, “Zero structures of n-D systems,” International Journal of Control, vol. 78, no. 4, pp. 277–285, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. E. Fornasini and G. Marchesini, “Doubly-indexed dynamical systems: State-space models and structural properties,” Mathematical Systems Theory, vol. 12, no. 1, pp. 59–72, 1978. View at Publisher · View at Google Scholar · View at Scopus
  19. M. Morf, B. C. Levy, and S. Y. Kung, “New results in 2-D systems theory: part II: state-space models—realization and the notions of controllability, observability, and minimality,” Proceedings of the IEEE, vol. 65, no. 6, pp. 945–961, 1977. View at Google Scholar · View at Scopus
  20. T. Kaczorek, Two-Dimensional Linear Systems, Springer, London, UK, 1985.
  21. T. Kaczorek, “Equivalence of singular 2-D linear models,” Bulletin of the Polish Academy of Sciences-Technical Sciences, vol. 37, no. 5-6, pp. 263–267, 1989. View at Google Scholar