Infinite elementary divisor structure-preserving transformations for polynomial matrices

Nicholas Karampetakis; Stavros Vologiannidis

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 4, page 493-503
  • ISSN: 1641-876X

Abstract

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The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where some conditions between the 1-D polynomial matrices and their transforming matrices are proposed.

How to cite

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Karampetakis, Nicholas, and Vologiannidis, Stavros. "Infinite elementary divisor structure-preserving transformations for polynomial matrices." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 493-503. <http://eudml.org/doc/207661>.

@article{Karampetakis2003,
abstract = {The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where some conditions between the 1-D polynomial matrices and their transforming matrices are proposed.},
author = {Karampetakis, Nicholas, Vologiannidis, Stavros},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {transformation; equivalence; autoregressive representations; infinite elementary divisors},
language = {eng},
number = {4},
pages = {493-503},
title = {Infinite elementary divisor structure-preserving transformations for polynomial matrices},
url = {http://eudml.org/doc/207661},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Karampetakis, Nicholas
AU - Vologiannidis, Stavros
TI - Infinite elementary divisor structure-preserving transformations for polynomial matrices
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 4
SP - 493
EP - 503
AB - The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where some conditions between the 1-D polynomial matrices and their transforming matrices are proposed.
LA - eng
KW - transformation; equivalence; autoregressive representations; infinite elementary divisors
UR - http://eudml.org/doc/207661
ER -

References

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  1. Antoniou E. and Vardulakis A. (2003): Fundamental equivalence of discrete-time AR-representations. - Int. J. Contr., Vol. 76, No. 11, pp. 1078-1088. Zbl1066.93011
  2. Antoniou E.N., Vardulakis A.I.G. and Karampetakis N.P. (1998): A spectral characterization of the behavior of discrete time AR-representations over a finite time interval. - Kybernetika, Vol. 34, No. 5, pp. 555-564. Zbl1274.93174
  3. Gantmacher F. (1959): The Theory of Matrices. -New York: Chelsea Pub.Co. Zbl0085.01001
  4. Gohberg I., Lancaster P. and Rodman L. (1982): Matrix Polynomials. -New York: Academic Press. Zbl0482.15001
  5. Hayton G.E., Pugh A.C. and Fretwell P. (1988): Infinite elementary divisors of a matrix polynomial and implications. - Int. J. Contr., Vol. 47, No. 1, pp. 53-64. Zbl0661.93016
  6. Johnson D. (1993): Coprimeness in multidimensional system theory and symbolic computation. -Ph.D. thesis, Loughborough University of Technology, U.K. 
  7. Karampetakis N. (2002a): On the determination of the dimension of the solution space of discrete time AR-representations. - Proc. 15th IFAC World Congress, Barcelona, Spain, (CD-ROM). 
  8. Karampetakis N. (2002b): On the construction of the forward and backward solution space of a discrete time AR-representation. - Proc. 15th IFAC World Congress, Barcelona, Spain, (CD-ROM). 
  9. Karampetakis N.P., Pugh A.C. and Vardulakis A.I. (1994): Equivalence transformations of rational matrices and applications. - Int. J. Contr., Vol. 59, No. 4, pp. 1001-1020. Zbl0813.93021
  10. Karampetakis N.P., Vologiannidis S. and Vardulakis A. (2002): Notions of equivalence for discrete time AR-representations. - Proc. 15th IFAC World Congress, Barcelona, Spain, (CD-ROM). Zbl1059.93027
  11. Levy B. (1981): 2-D polynomial and rational matrices and their applications for the modelling of 2-D dynamical systems. -Ph.D. thesis, Stanford University, U.S.A. 
  12. Praagman C. (1991): Invariants of polynomial matrices. - Proc. 1st European Control Conf., Grenoble, France, pp. 1274-1277, 
  13. Pugh A.C. and El-Nabrawy E.M.O. (2003): Zero Structures of N-D Systems. - Proc. 11th IEEE Mediterranean Conf. Control and Automation, Rhodes, Greece, (CD-ROM). Zbl1213.93070
  14. Pugh A.C. and Shelton A.K. (1978): On a new definition of strict system equivalence. - Int. J. Contr., Vol. 27, No. 5, pp. 657-672. Zbl0393.93010
  15. Vardulakis A. (1991): Linear Multivariable Control: Algebraic Analysis, and Synthesis Methods. - Chichester: Willey. Zbl0751.93002
  16. Vardulakis A. and Antoniou E. (2001): Fundamental equivalence of discrete time ar representations. - Proc. 1st IFAC Symp. System Structure and Control, Prague, Czech Republic, (CD-ROM). Zbl1066.93011

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