An equivalent matrix pencilfor bivariate polynomial matrices
Boudellioua, Mohamed
International Journal of Applied Mathematics and Computer Science, Tome 16 (2006), p. 175-181 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:207782
@article{bwmeta1.element.bwnjournal-article-amcv16i2p175bwm,
     author = {Boudellioua, Mohamed},
     title = {An equivalent matrix pencilfor bivariate polynomial matrices},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {16},
     year = {2006},
     pages = {175-181},
     zbl = {1113.15013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv16i2p175bwm}
}
Boudellioua, Mohamed. An equivalent matrix pencilfor bivariate polynomial matrices. International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) pp. 175-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv16i2p175bwm/

[000] Blomberg H. and Ylinen R. (1983): Algebraic Theory for Multivariable Linear Systems. - London: Academic Press. | Zbl 0556.93016

[001] Fuhrmann P.A. (1977): On strict system equivalence and similarity. -Int. J. Contr., Vol. 25, No. 1, pp. 5-10. | Zbl 0357.93009

[002] 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. | Zbl 0702.93021

[003] Johnson D.S. (1993): Coprimeness in multidimensional system theory and symbolic computation. - Ph.D. thesis, Loughborough University of Technology, UK.

[004] 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. | Zbl 0655.93046

[005] 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. | Zbl 0859.93024

[006] 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.

[007] Oberst U. (1990): Multidimensional constant linear systems. - Acta Applicande Mathematicae, Vol. 20, pp. 1-175. | Zbl 0715.93014

[008] Polderman J.W. and Willems J.C. (1998): Introduction to Mathematical System Theory: A Behavioral Approach. - New York: Springer. | Zbl 0940.93002

[009] 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.

[010] 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. | Zbl 0951.93039

[011] 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. | Zbl 0987.93010

[012] 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. | Zbl 1213.93070

[013] 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. | Zbl 1213.93070

[014] Rosenbrock H.H. (1970): State Space and Multivariable Theory. - London: Nelson-Wiley. | Zbl 0246.93010

[015] Sontag E.D. (1980): On generalized inverses of polynomial and other matrices. -IEEE Trans. Automat. Contr., Vol. AC-25, No. 3, pp. 514-517. | Zbl 0447.15003

[016] Verghese G.C. (1978): Infinite-frequency behaviour in generalized dynamical systems. -Ph.D. thesis, Stanford University, USA.

[017] Wolovich W.A. (1974): Linear Multivariable Systems. -New York: Springer. | Zbl 0291.93002

[018] 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. | Zbl 0394.93004

[019] Zerz E. (1996): Primeness of multivariate polynomial matrices. -Syst. Contr. Lett., Vol. 29, pp. 139-145. | Zbl 0866.93053