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

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 2, page 231-234
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Kaczorek, Tadeusz. "Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays." International Journal of Applied Mathematics and Computer Science 15.2 (2005): 231-234. <http://eudml.org/doc/207738>.

@article{Kaczorek2005,
abstract = {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.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Cayley-Hamilton theorem; continuous-time; delay; linear system; extension},
language = {eng},
number = {2},
pages = {231-234},
title = {Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays},
url = {http://eudml.org/doc/207738},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 2
SP - 231
EP - 234
AB - 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.
LA - eng
KW - Cayley-Hamilton theorem; continuous-time; delay; linear system; extension
UR - http://eudml.org/doc/207738
ER -

References

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  1. 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). Zbl1140.93450
  2. 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 
  3. Gałkowski K. (1996): Matrix description of multivariable polynomials. - Lin. Alg. and Its Applic., Vol. 234, No. 2, pp. 209-226. Zbl0849.93033
  4. Gantmacher F.R. (1974): The Theory of Matrices. - Vol. 2.-Chelsea: New York. Zbl0085.01001
  5. Kaczorek T. (19921993): Linear Control Systems. -Vols. I, II, Tauton: Research Studies Press. Zbl0784.93002
  6. 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. Zbl0823.93032
  7. 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. Zbl0845.93042
  8. 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. Zbl0837.15012
  9. 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. 
  10. 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. Zbl0914.15011
  11. Kaczorek T. (2005): Generalization of Cayley-Hamilton theorem for n-D polynomial matrices. - IEEE Trans. Automat. Contr., No. 5, (in press). 
  12. Lancaster P. (1969): Theory of Matrices. -New York, Academic, Press. Zbl0186.05301
  13. 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. 
  14. 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. Zbl0601.15010
  15. 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. 
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