Equivalence and reduction of delay-differential systems

• Autorzy: Boudellioua M. S.
• Języki publikacji: EN

Abstrakty

EN

A new direct method is presented which reduces a given high-order representation of a control system with delays to a firstorder form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann’s strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant.

Słowa kluczowe

EN

polynomial matrix description; neutral delay-differential systems; strict system equivalence; determinantal ideals; Gröbner bases

PL

opis macierzowy; układ z opóźnieniem; równoważność systemu; bazy Gröbnera

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: Vol. 17, no 1
• Strony: 15--22
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Boudellioua M. S.

• Department of Mathematics and Statistics Sultan Qaboos University, PO Box 36 Al-Khodh, 123, Muscat, Oman,

Bibliografia

• [1] Boudellioua M.S. (2006): An equivalent matrix pencil for bivariate polynomial matrices. - Int. J. Appl. Math. Comput. Sci., Vol. 16, No. 2, pp. 175-181.
• [2] Byrnes C.I., Spong M.W. and Tarn T.J. (1984): A several complex variables approach to feedback stabilization of linear neutral delay-differential systems. - Math. Syst. Theory, Vol. 17, No. 2, pp. 97-133.
• [3] Fuhrmann P.A. (1977): On strict system equivalence and similarity. - Int. J. Contr., Vol. 25, No. 1, pp.5-10.
• [4] Johnson D.S. (1993): Coprimeness in multidimensional system theory and symbolic computation. -Ph.D. thesis, Loughborough University of Technology, UK.
• [5] 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.
• [6] 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.
• [7] Pugh A.C.,McInerney S.J., Boudellioua M.S., Johnson D.S. and Hayton G.E. (1998b): 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.
• [8] 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.
• [9] 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.
• [10] Pugh A.C., McInerney S.J., Hou M. and Hayton G.E. (1996): A transformation for 2-D systems and its invariants. - Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan, pp. 2157-2158.
• [11] Rosenbrock H.H. (1970): State Space and Multivariable Theory. - London: Nelson-Wiley.
• [12] Sebek M. (1988): One more counterexample in n-D systems - Unimodular versus elementary operations.-IEEE Trans. Autom. Contr., Vol. AC-33(5), pp. 502-503.
• [13] Zerz E. (2000): Topics in Multidimensional Linear Systems Theory. - London: Springer.