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2006 | 16 | 1 | 141-145
Tytuł artykułu

An extension of the Cayley-Hamilton theorem for nonlinear time-varying systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The classical Cayley-Hamilton theorem is extended to nonlinear time-varying systems with square and rectangular system matrices. It is shown that in both cases system matrices satisfy many equations with coefficients being the coefficients of characteristic polynomials of suitable square matrices. The proposed theorems are illustrated with numerical examples.
Rocznik
Tom
16
Numer
1
Strony
141-145
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-08-10
poprawiono
2005-09-15
Twórcy
  • Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45 D, 15-351 Białystok, Poland
Bibliografia
  • Busłowicz M. (1981): An algorithm of determination of the quasi-polynomial of multivariable time-invariant linear system with delays based on state equations. - Archive of Automatics and Telemechanics, Vol. XXXVI, No. 1, pp. 125-131, (in Polish).
  • Busłowicz M. (1982): Inversion of characteristic matrix of the time-delay systems of neural type. - Found. Contr. Eng.,Vol. 7, No. 4, pp. 195-210.
  • Busłowicz M. and Kaczorek T. (2004): Rechability and minimum energy control of positive linear discrete-time systems with one delay. - Proc. 12th Mediterranean Conf. Control and Automation, Kasadasi-Izmur, Turkey (on CD-ROM).
  • Chang F.R. and Chan C.N. (1992): The generalized Cayley-Hamilton theorem for standard pencils. - Syst. Contr.Lett., Vol. 18, No. 3, pp. 179-182.
  • Gantmacher F.R. (1974): The Theory of Matrices. - Vol. 2, Chelsea.
  • Kaczorek T. (1988): Vectors and Matrices in Automation and Electrotechnics. - Warsaw: Polish Scientific Publishers, (in Polish).
  • Kaczorek T. (1992-1993): Linear Control Systems, Vols. I and II. - Taunton: Research Studies Press.
  • Kaczorek T. (1994): Extensions of the Cayley-Hamilton theorem for 2D continuous-discrete linear systems. - Appl. Math. Comput. Sci.,Vol. 4, No. 4, pp. 507-515.
  • Kaczorek T. (1995a): An existence of the Cayley-Hamilton theorem for singular 2D linear systems with non-square matrices. - Bull. Pol. Acad. Techn.Sci., Vol. 43, No. 1, pp. 39-48.
  • Kaczorek T. (1995b): An existence of the Cayley-Hamilton theorem for nonsquare block matrices. - Bull. Pol. Acad. Techn. Sci.,Vol. 43, No. 1, pp. 49-56.
  • Kaczorek T. (1995c): Generalization of the Cayley-Hamilton theorem for nonsquare matrices. - Proc. Int. Conf. Fundamentals of Electrotechnics and Circuit Theory XVIII-SPETO, Gliwice, Poland, pp. 77-83.
  • Kaczorek T. (1998): An extension of the Cayley-Hamilton theorem for a standard pair of block matrices. - Appl. Math. Com. Sci., Vol. 8, No. 3, pp. 511-516.
  • Kaczorek T. (2005a): Generalization of Cayley-Hamilton theorem for n-D polynomial matrices. - IEEE Trans. Automat Contr., Vol. 50, No. 5, pp. 671-674.
  • Kaczorek T. (2005b): Extension of the Cayley-Hamilton theorem for continuous-time systems with delays. - Appl. Math. Comp. Sci., Vol. 15, No. 2, pp. 231-234.
  • Lancaster P. (1969): Theory of Matrices. - New York: Acad. Press.
  • Lewis F.L. (1982): Cayley-Hamilton theorem and Fadeev's method for the matrix pencil [sE-A]. - Proc. 22nd IEEE Conf. Decision and Control, San Diego, USA, pp. 1282-1288.
  • Lewis F.L. (1986): Further remarks on the Cayley-Hamilton theorem and Fadeev's method for the matrix pencil [sE-A]. - IEEE Trans. Automat. Contr.,Vol. 31, No. 7, pp. 869-870.
  • Mcrtizios B.G. and Christodolous M.A. (1986): On the generalized Cayley-Hamilton theorem. - IEEE Trans. Automat. Contr., Vol. 31, No. 1, pp. 156-157.
  • Smart N.M. and Barnett S. (1989): The algebra of matrices in n-dimensional systems. - IMA J. Math. Contr. Inf., Vol. 6, pp. 121-133.
  • Theodoru N.J. (1989): M-dimensional Cayley-Hamilton theorem. - IEEE Trans. Automat. Control, Vol. AC-34, No. 5, pp. 563-565.
  • Victoria J. (1982): A block Cayley-Hamilton theorem. - Bull. Math. Soc. Sci. Math. Roum, Vol. 26, No. 1, pp. 93-97.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv16i1p141bwm
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