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2006 | 16 | 2 | 175-181
Tytuł artykułu

An equivalent matrix pencilfor bivariate polynomial matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
16
Numer
2
Strony
175-181
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-05-07
poprawiono
2005-11-21
Twórcy
  • Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, Al-Khodh, 123, Muscat, Oman
Bibliografia
  • Blomberg H. and Ylinen R. (1983): Algebraic Theory for Multivariable Linear Systems. - London: Academic Press.
  • Fuhrmann P.A. (1977): On strict system equivalence and similarity. -Int. J. Contr., Vol. 25, No. 1, pp. 5-10.
  • 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.
  • Johnson D.S. (1993): Coprimeness in multidimensional system theory and symbolic computation. - Ph.D. thesis, Loughborough University of Technology, UK.
  • 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.
  • 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.
  • 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.
  • Oberst U. (1990): Multidimensional constant linear systems. - Acta Applicande Mathematicae, Vol. 20, pp. 1-175.
  • Polderman J.W. and Willems J.C. (1998): Introduction to Mathematical System Theory: A Behavioral Approach. - New York: Springer.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Rosenbrock H.H. (1970): State Space and Multivariable Theory. - London: Nelson-Wiley.
  • Sontag E.D. (1980): On generalized inverses of polynomial and other matrices. -IEEE Trans. Automat. Contr., Vol. AC-25, No. 3, pp. 514-517.
  • Verghese G.C. (1978): Infinite-frequency behaviour in generalized dynamical systems. -Ph.D. thesis, Stanford University, USA.
  • Wolovich W.A. (1974): Linear Multivariable Systems. -New York: Springer.
  • 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.
  • Zerz E. (1996): Primeness of multivariate polynomial matrices. -Syst. Contr. Lett., Vol. 29, pp. 139-145.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv16i2p175bwm
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