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2003 | 13 | 4 | 493-503
Tytuł artykułu

Infinite elementary divisor structure-preserving transformations for polynomial matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
13
Numer
4
Strony
493-503
Opis fizyczny
Daty
wydano
2003
otrzymano
2003-03-05
poprawiono
2003-09-03
Twórcy
  • Department of Mathematics, Aristotle University of Thessalonika, Thessalonika 54006, Greece
  • Department of Mathematics, Aristotle University of Thessalonika, Thessalonika 54006, Greece
Bibliografia
  • Antoniou E. and Vardulakis A. (2003): Fundamental equivalence of discrete-time AR-representations. - Int. J. Contr., Vol. 76, No. 11, pp. 1078-1088.
  • 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.
  • Gantmacher F. (1959): The Theory of Matrices. -New York: Chelsea Pub.Co.
  • Gohberg I., Lancaster P. and Rodman L. (1982): Matrix Polynomials. -New York: Academic Press.
  • 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.
  • Johnson D. (1993): Coprimeness in multidimensional system theory and symbolic computation. -Ph.D. thesis, Loughborough University of Technology, U.K.
  • 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).
  • 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).
  • 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.
  • 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).
  • 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.
  • Praagman C. (1991): Invariants of polynomial matrices. - Proc. 1st European Control Conf., Grenoble, France, pp. 1274-1277,
  • 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).
  • 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.
  • Vardulakis A. (1991): Linear Multivariable Control: Algebraic Analysis, and Synthesis Methods. - Chichester: Willey.
  • 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).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i4p493bwm
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