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Journal of Control Science and Engineering
Volume 2007 (2007), Article ID 87171, 5 pages
Research Article

Controllable and Observable Polynomial Description for 2D Noncausal Systems

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

Received 26 February 2007; Accepted 19 May 2007

Academic Editor: Tongwen Chen

Copyright © 2007 M. 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. N. K. Bose, Applied Multidimensional Systems Theory, Van Nostrand Reinhold, New York, NY, USA, 1982.
  2. H. H. Rosenbrock, State Space and Multivariable Theory, Nelson-Wiley, New York, NY, USA, 1970.
  3. 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.
  4. M. G. Frost and M. S. Boudellioua, “Further observations concerning the strict system equivalence of polynomial system matrices over [s,z],” International Journal of Control, vol. 49, no. 1, pp. 1–14, 1989.
  5. D. S. Johnson, Coprimeness in multidimensional system theory and symbolic computation, Ph.D. thesis, Loughborough University of Technology, Leics, UK, 1993.
  6. A. C. Pugh, S. J. Mcinerney, M. S. Bouoellioua, 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 Publisher · View at Google Scholar · View at MathSciNet
  7. S. Attasi, “Systemes lineaires a deux indices,” Tech. Rep. 31, IRIA, Le Chesnay, France, 1973.
  8. 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 Publisher · View at Google Scholar
  9. R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Transactions on Automatic Control, vol. 20, no. 1, pp. 1–75, 1975.
  10. S.-Y. Kung, B. C. Levy, 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,” Proceedings of the IEEE, vol. 65, no. 6, pp. 945–961, 1977.
  11. E. Zerz, Topics in Multidimensional Linear Systems Theory, Springer, London, UK, 2000.
  12. S. H. Zak, “On state-space models for systems described by partial differential equations,” in Proceedings of the 33rd IEEE Conference on Decision and Control (CDC '84), pp. 571–576, Las Vegas, Nev, USA, December 1984.
  13. T. Kaczorek, Two-Dimensional Linear Systems, Springer, London, UK, 1985.
  14. T. Kaczorek, “Singular models of 2-D systems,” in Proceedings of the 12th World Congress on Scientific Computation, Paris, France, July 1988.
  15. K. Galkowski, State-Space Realizations of Linear 2-D Systems with Extensions to the General nD(n>2) Case, Springer, London, UK, 2001.
  16. T. Kaczorek, Polynomial and Rational Matrices: Applications in Dynamical Systems Theory, Springer, London, UK, 2006.
  17. Y. Zou and S. L. Campbell, “The jump behavior and stability analysis for 2-D singular systems,” Multidimensional Systems and Signal Processing, vol. 11, no. 4, pp. 321–338, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. H. Xu, L. Xie, S. Xu, and Y. Zou, “Positive real control for uncertain 2-D singular Roesser models,” International Journal of Control, Automation and Systems, vol. 3, no. 2, pp. 195–201, 2005.
  19. G. C. Verghese, B. C. Levy, and T. Kailath, “A generalized state-space for singular systems,” IEEE Transactions on Automatic Control, vol. 26, no. 4, pp. 811–831, 1981. View at Publisher · View at Google Scholar
  20. F. R. Gantmacher, The Theory of Matrices, Chelsea, London, UK, 1971.
  21. R. Eising, 2-D Systems, an Algebraic Approach, Mathematical Centre Tracts, Amsterdam, The Netherland, 1980.