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Autor
Boudellioua Mohamed S. (Sultan Qaboos University, Muscat, Oman)
Tytuł
Further Results on the Equivalence to Smith Form of Multivariate Polynomial Matrices
Źródło
Control and Cybernetics, 2013, vol. 42, nr 2, s. 543-551, bibliogr. s. 551
Słowa kluczowe
Teoria systemów, Zastosowanie matematyki, Teoria kontroli
Theory of systems, Applications of mathematics, Control theory
Uwagi
summ.
Abstrakt
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. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej
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Bibliografia
Pokaż
  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.
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ISSN
0324-8569
Język
eng
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