Further Results on the Equivalence to Smith Form of Multivariate Polynomial Matrices

• Autorzy: Mohamed S. Boudellioua
• 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. (original abstract)

Słowa kluczowe

PL

Teoria systemów; Zastosowanie matematyki; Teoria kontroli

EN

Theory of systems; Applications of mathematics; Control theory

• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: 42
• Numer: nr 2
• Strony: 543-551

Twórcy

autor

Mohamed S. Boudellioua

• Sultan Qaboos University, Muscat, Oman

Bibliografia

• Boudellioua, M.S. and Quadrat, A. (2010) Serre's reduction of linear functional systems. Mathematics in Computer Science 4(2), 289-312.
• Boudellioua, M.S. (2012) Computation of the Smith form for multivariate polynomial matrices using Maple. American J. of Computational Mathematics 2(1), 21-26.
• 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.
• 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.
• 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.
• 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.
• 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.
• Lee, E. and Zak, S. (1983) Smith forms over R[z1, z2]. IEEE Trans. Autom. Control 28(1), 115-118.
• 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.
• Lin, Z. and Bose, N. (2001) A generalization of Serre's conjecture and related issues. Linear Algebra and its Applications 338(2001), 125-138.
• 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.
• 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.
• Rosenbrock, H. H. (1970) State Space and Multivariable Theory. Nelson- Wiley, London-New York.