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2005 | 15 | 2 | 231-234
Tytuł artykułu

Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.
Rocznik
Tom
15
Numer
2
Strony
231-234
Opis fizyczny
Daty
wydano
2005
otrzymano
2005-03-30
poprawiono
2005-05-04
Twórcy
  • Institute of Control and Industrial Electronics,Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
Bibliografia
  • Busłowicz M. and Kaczorek T. (2004): Reachability and minimum energy control of positive linear discrete-time systems with one delay. - Proc. 12-th Mediterranean Conf. s Control and Automation, Kasadasi, Turkey: Izmir (on CD-ROM).
  • Chang F.R. and Chan C.N. (1992): The generalized Cayley-Hamilton theorem for standard pencis. - Syst. Contr. Lett., Vol. 18, No. 192, pp. 179-182
  • Gałkowski K. (1996): Matrix description of multivariable polynomials. - Lin. Alg. and Its Applic., Vol. 234, No. 2, pp. 209-226.
  • Gantmacher F.R. (1974): The Theory of Matrices. - Vol. 2.-Chelsea: New York.
  • Kaczorek T. (19921993): Linear Control Systems. -Vols. I, II, Tauton: 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 nonsquareblock matrices and computation of the left and right inverses of 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, Ustron-Gliwice, Poland, pp. 77-83.
  • Kaczorek T. (1998): An extension of the Cayley-Hamilton theorem for a standard pair of block matrices. - Appl. Math. Comput. Sci., Vol. 8, No. 3, pp. 511-516.
  • Kaczorek T. (2005): Generalization of Cayley-Hamilton theorem for n-D polynomial matrices. - IEEE Trans. Automat. Contr., No. 5, (in press).
  • Lancaster P. (1969): Theory of Matrices. -New York, Academic, 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.
  • Mertizios B.G and Christodoulous 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. - Math. Contr. Inf., Vol. 6, No. 1, pp. 121-133.
  • Theodoru N.J. (1989): M-dimensional Cayley-Hamilton theorem. - IEEE Trans. Automat. Contr., 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-amcv15i2p231bwm
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