Table of Contents
International Journal of Computational Mathematics
Volume 2014, Article ID 487465, 6 pages
Research Article

Computation of a Canonical Form for Linear 2D Systems

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

Received 8 July 2014; Revised 19 November 2014; Accepted 27 November 2014; Published 15 December 2014

Academic Editor: Anh-Huy Phan

Copyright © 2014 Mohamed Salah 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. S. Barnett, “A matrix circle in linear control theory,” Bulletin of the Institute of Mathematics and Its Applications, vol. 12, no. 6, pp. 173–176, 1976. View at Google Scholar
  2. M. S. Boudellioua, “A canonical matrix representation of 2-D linear discrete systems,” Journal for Engineering Sciences, vol. 11, no. 2, pp. 81–90, 1999. View at Google Scholar
  3. 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 Publisher · View at Google Scholar
  4. F. Chyzak, A. Quadrat, and D. Robertz, “OreModules: a symbolic package for the study of multidimensional linear systems,” in Applications of Time-Delay Systems, J. Chiasson and and J.-J. Loiseau, Eds., vol. 352 of Lecture Notes in Control and Information Sciences, pp. 233–264, Springer, 2007, / View at Google Scholar
  5. S. Attasi, “Systemes lineaires a deux indices,” Tech. Rep. 31, IRIA, Paris, France, 1973. View at Google Scholar
  6. E. Fornasini and G. Marchesini, “State-space realization theory of two-dimensional filters,” IEEE Transactions on Automatic Control, vol. 21, no. 4, pp. 484–492, 1976. View at Google Scholar
  7. H. H. Rosenbrock, State-Space and Multivariable Theory, John Wiley & Sons, London, UK, 1970.
  8. M. G. Frost and C. Storey, “Equivalence of a matrix over R[s; z] with its Smith form,” International Journal of Control, vol. 28, no. 5, pp. 665–671, 1978. View at Google Scholar
  9. M. G. Frost and M. S. Boudellioua, “Some further results concerning matrices with elements in a polynomial ring,” International Journal of Control, vol. 43, no. 5, pp. 1543–1555, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. E. B. Lee and S. H. Zak, “Smith forms over Rz1,z2,” IEEE Transactions on Automatic Control, vol. 28, no. 1, pp. 115–118, 1983. View at Google Scholar
  11. Z. Lin, M. S. Boudellioua, and L. Xu, “On the Equivalence and Factorization of Multivariate Polynomial Matrices,” in Proceedings of the IEEE International Symposium on Circuits and Systems, pp. 4911–4914, Island of Kos, Greece, May 2006.
  12. M. S. Boudellioua and A. Quadrat, “Serre's reduction of linear functional systems,” Mathematics in Computer Science, vol. 4, no. 2, pp. 289–312, 2010. View at Google Scholar
  13. A. Fabianska and A. Quadrat, “Applications of the Quillen-Suslin theorem in multidimensional systems theory,” in Grobner Bases in Control Theory and Signal Processing, H. Park and G. Regensburger, Eds., vol. 3 of Radon Series on Computation and Applied Mathematics, pp. 23–106, de Gruyter publisher, 2007. View at Google Scholar
  14. D. Quillen, “Projective modules over polynomial rings,” Inventiones Mathematicae, vol. 36, pp. 167–171, 1976. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. A. A. Suslin, “Projective modules over polynomial rings are free,” Soviet Mathematics—Doklady, vol. 17, no. 4, pp. 1160–1164, 1976. View at Google Scholar
  16. E. Zerz, Topics in Multidimensional Linear Systems Theory, Springer, London, UK, 2000.