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Further results on the equivalence to Smith form of multivariate polynomial matrices

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Języki publikacji
EN
Abstrakty
EN
Multivariate polynomial matrices arise from the treatment of linear systems of partial differential equations, delay-differential equations or multidimensional discrete equations. In this paper we generalize some of the results obtained for the equivalence to the Smith normal form for a class of multivariate polynomial matrices.
Rocznik
Strony
543--551
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
  • Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, Al-Khodh, 123, Muscat, Oman
Bibliografia
  • 1. Boudellioua, M.S. and Quadrat, A. (2010) Serre’s reduction of linear functional systems. Mathematics in Computer Science 4(2), 289–312.
  • 2. Boudellioua, M.S. (2012) Computation of the Smith form for multivariate polynomial matrices using Maple. American J. of Computational Mathematics 2(1), 21–26.
  • 3. Chyzak, F., Quadrat, A. and Robertz, D. (2007) OreModules: A symbolic package for the study of multidimensional linear systems. In: J., Chiasson and J.-J., Loiseau, eds., Applications of Time-Delay Systems LNCIS 352, Springer, 233–264.
  • 4. Chyzak, F. and Robertz, D. (2005) Effective algorithms for parametrizing linear control systems over ore algebras. Applicable Algebra in Engineering, Communication and Computing 16(5), 319–376.
  • 5. Fabiańska, A. and Quadrat, A. (2007) Applications of the Quillen-Suslin theorem in multidimensional systems theory. In: H. Park and G. Regensburger, eds., Gröbner Bases in Control Theory and Signal Processing. Radon Series on Computation and Applied Mathematics 3. de Gruyter, 23–106.
  • 6. Frost, M.G. and Boudellioua, M.S. (1986) Some further results concerning matrices with elements in a polynomial ring. Int. J. Control 43(5), 1543–1555.
  • 7. Frost, M.G. and Storey, C. (1979) Equivalence of a matrix over R[s, z] with its Smith form. Int. J. Control 28(5), 665–671.
  • 8. Lee, E. and Zak, S. (1983) Smith forms over R[z1, z2]. IEEE Trans. Autom. Control 28(1), 115–118.
  • 9. Levandovskyy, V. and Zerz, E. (2007) Obstructions to genericity in the study of parametric problems in control theory. In: H. Park and G. Regensburger, eds., Gröbner Bases in Control Theory and Signal Processing. Radon Series on Computation and Applied Mathematics 3. de Gruyter, 127–149.
  • 10. Lin, Z. and Bose, N. (2001) A generalization of Serre’s conjecture and related issues. Linear Algebra and its Applications 338(2001), 125–138.
  • 11. Lin, Z., Boudellioua, M.S. and Xu, L. (2006) On the equivalence and factorization of multivariate polynomial matrices. In: Proceedings of the 2006 international symposium of circuits and systems, Island of Kos (Greece). IEEE, 4914–4917.
  • 12. Pommaret, J.-F. and Quadrat, A. (2000) Formal elimination for multidimensional systems and applications to control theory. Mathematics of Control, Signal and Systems 13(4), 193–215.
  • 13. Rosenbrock, H. H. (1970) State Space and Multivariable Theory. Nelson- Wiley, London–New York.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-3665cac4-c026-4d27-9c3f-f0797f6fabf6
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