An equivalent matrix pencilfor bivariate polynomial matrices

Mohamed Boudellioua

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 2, page 175-181
  • ISSN: 1641-876X

Abstract

top
In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

How to cite

top

Boudellioua, Mohamed. "An equivalent matrix pencilfor bivariate polynomial matrices." International Journal of Applied Mathematics and Computer Science 16.2 (2006): 175-181. <http://eudml.org/doc/207782>.

@article{Boudellioua2006,
abstract = {In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.},
author = {Boudellioua, Mohamed},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {invariant polynomials; matrix pencils; 2-D singular systems; invariant zeros; zero-coprime-equivalence; matrix pencil; bivariate polynomial matrix},
language = {eng},
number = {2},
pages = {175-181},
title = {An equivalent matrix pencilfor bivariate polynomial matrices},
url = {http://eudml.org/doc/207782},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Boudellioua, Mohamed
TI - An equivalent matrix pencilfor bivariate polynomial matrices
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 2
SP - 175
EP - 181
AB - In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.
LA - eng
KW - invariant polynomials; matrix pencils; 2-D singular systems; invariant zeros; zero-coprime-equivalence; matrix pencil; bivariate polynomial matrix
UR - http://eudml.org/doc/207782
ER -

References

top
  1. Blomberg H. and Ylinen R. (1983): Algebraic Theory for Multivariable Linear Systems. - London: Academic Press. Zbl0556.93016
  2. Fuhrmann P.A. (1977): On strict system equivalence and similarity. -Int. J. Contr., Vol. 25, No. 1, pp. 5-10. Zbl0357.93009
  3. Hayton G.E., Walker A.B. and Pugh A.C. (1990): Infinite frequency structure-preserving transformations for general polynomial system matrices. -Int. J. Contr., Vol. 33, No. 52, pp. 1-14. Zbl0702.93021
  4. Johnson D.S. (1993): Coprimeness in multidimensional system theory and symbolic computation. - Ph.D. thesis, Loughborough University of Technology, UK. 
  5. Kaczorek T. (1988): The singular general model of 2-D systems and its solution. -IEEE Trans. Automat. Contr., Vol. 33, No. 11, pp. 1060-1061. Zbl0655.93046
  6. Karampetakis N.K., Vardulakis A.I. and Pugh A.C. (1995): A classification of generalized state-space reduction methods for linear multivariable systems. - Kybernetica, Vol. 31, No. 6, pp. 547-557. Zbl0859.93024
  7. Levy B.C. (1981): 2-D polynomial and rational matrices and their applications for the modelling of 2-D dynamical systems. - Ph.D. thesis, Stanford University, USA. 
  8. Oberst U. (1990): Multidimensional constant linear systems. - Acta Applicande Mathematicae, Vol. 20, pp. 1-175. Zbl0715.93014
  9. Polderman J.W. and Willems J.C. (1998): Introduction to Mathematical System Theory: A Behavioral Approach. - New York: Springer. Zbl0940.93002
  10. Pugh A.C., McInerney S.J., Hou M. and Hayton G.E. (1996): A transformation for 2-D systems and its invariants. -Proc. 35-th IEEE Conf. Decision and Control, Kobe, Japan, pp. 2157-2158. 
  11. Pugh A.C., McInerney S.J., Boudellioua M.S. and Hayton G.E. (1998a): Matrix pencil equivalents of a general 2-D polynomial matrix. - Int. J. Contr., Vol. 71, No. 6, pp. 1027-1050. Zbl0951.93039
  12. Pugh A.C., McInerney S.J., Boudellioua M.S., Johnson D.S. and Hayton G.E. (1998): A transformation for 2-D linear systems and a generalization of a theorem of Rosenbrock. - Int. J. Contr., Vol. 71, No. 3, pp. 491-503. Zbl0987.93010
  13. Pugh A.C., McInerney S.J. and El-Nabrawy E.M.O. (2005a): Equivalence and reduction of 2-D systems. -IEEE Trans. Circ. Syst., Vol. 52, No. 5, pp. 371-275. Zbl1213.93070
  14. Pugh A.C., McInerney S.J. and El-Nabrawy E.M.O. (2005b): Zero structures of n-D systems. -Int. J. Contr., Vol. 78, No. 4, pp. 277-285. Zbl1213.93070
  15. Rosenbrock H.H. (1970): State Space and Multivariable Theory. - London: Nelson-Wiley. Zbl0246.93010
  16. Sontag E.D. (1980): On generalized inverses of polynomial and other matrices. -IEEE Trans. Automat. Contr., Vol. AC-25, No. 3, pp. 514-517. Zbl0447.15003
  17. Verghese G.C. (1978): Infinite-frequency behaviour in generalized dynamical systems. -Ph.D. thesis, Stanford University, USA. 
  18. Wolovich W.A. (1974): Linear Multivariable Systems. -New York: Springer. Zbl0291.93002
  19. Youla D.C. and Gnavi G. (1979): Notes on n-dimensional system theory. -IEEE Trans. Circ. Syst., Vol. CAS-26, No. 2, pp. 105-111. Zbl0394.93004
  20. Zerz E. (1996): Primeness of multivariate polynomial matrices. -Syst. Contr. Lett., Vol. 29, pp. 139-145. Zbl0866.93053

NotesEmbed ?

top

You must be logged in to post comments.