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Computation of a canonical form for neutral delay-differential systems

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Języki publikacji
EN
Abstrakty
EN
In this paper, symbolic computation techniques are used to obtain a canonical form for polynomial matrices arising from linear delay-differential systems of the neutral type. The canonical form can be regarded as an extension of the companion form, often encountered in the theory of linear systems, described by ordinary differential equations. Using the Smith normal form, the exact connection between the original polynomial matrix and the reduced canonical form is set out. An example is given to illustrate the computational aspects involved.
Rocznik
Strony
357--368
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
  • Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, Al-Khodh, 123, Muscat, Oman
Bibliografia
  • [1] Barnett, S. (1976) A matrix circle in control theory. I.M.A. Bulletin 12, 173-176.
  • [2] Boudellioua, M.S. (2007) On the eigenstructure assignment of delay-differential systems. Int. Journal of Contemp. Math. Sciences 2(20), 951-959.
  • [3] Boudellioua, M.S. and Quadrat, A. (2010) Serre's reduction of linear functional systems. Mathematics in Computer Science 4(2), 289-312.
  • [4] Byrnes, C.I., Spong, M.W. and Tarn, T.J. (1984) A several complex variables approach to feedback stabilization of linear neutral delay-differential systems. Mathematical Systems Theory 17(2), 97-133.
  • [5] 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.
  • [6] Fabianska, A. and Quadrat, A. (2007) Applications of the Quillen-Suslin theorem in multidimensional systems theory. In: H. Park and G. Regensburger, eds., Grobner Bases in Control Theory and Signal Processing, Radon Series on Computation and Applied Mathematics 3, De Gruyter, 23-106.
  • [7] 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.
  • [8] 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.
  • [9] Lee, E.B. and Zak, S.H. (1983) Smith forms over R[21,z2]- IEEE Trans. Autom. Control 28(1), 115-118.
  • [10] 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., Grobner Bases in Control Theory and Signal Processing, Radon Series on Computation and Applied Mathematics 3, De Gruyter, 127-149.
  • [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, 4911-4914.
  • [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, 193-215.
  • [13] Quillen, D. (1976) Protective modules over polynomial rings. Invent. Math. 36,167-171.
  • [14] Rosenbrock, H.H. (1970) State space and multivariable theory. Nelson-Wiley, London, New York.
  • [15] Suslin, A.A. (1976) Protective modules over polynomial rings are free. Soviet Math. Dokl. 17(4), 1160-1164.
  • [16] Zerz, E. (2000) Topics in Multidimensional Linear Systems Theory. Springer, London.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ce0194a0-ea1b-4380-ab9f-b80be010dbfb
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