Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 2, page 369-376
  • ISSN: 1641-876X

Abstract

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A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.

How to cite

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Kaczorek, Tadeusz. "Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks." International Journal of Applied Mathematics and Computer Science 11.2 (2001): 369-376. <http://eudml.org/doc/207511>.

@article{Kaczorek2001,
abstract = {A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {elimination; finite eigenvalue; 2D Roesser model; state feedback; multivariable control systems; 2-D systems; linear discrete control systems; Roesser form; closed-loop characteristic polynomial; state feedbacks; elimination of finite eigenvalues},
language = {eng},
number = {2},
pages = {369-376},
title = {Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks},
url = {http://eudml.org/doc/207511},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 2
SP - 369
EP - 376
AB - A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.
LA - eng
KW - elimination; finite eigenvalue; 2D Roesser model; state feedback; multivariable control systems; 2-D systems; linear discrete control systems; Roesser form; closed-loop characteristic polynomial; state feedbacks; elimination of finite eigenvalues
UR - http://eudml.org/doc/207511
ER -

References

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  1. Dai L. (1988): Observers for discrete singular systems. - IEEE Trans. Automat. Contr., Vol. AC-33, No. 2, pp. 187-191. Zbl0633.93025
  2. Dai L. (1989): Singular Control Systems. - Berlin, Tokyo: Springer. Zbl0669.93034
  3. Fornasini E. and Marchesini G. (1976): State space realization of two-dimensional filters. - IEEE Trans. Automat. Contr., Vol. AC-21, No. 4, pp. 484-491. Zbl0332.93072
  4. Fornasini E. and Marchesini G. (1978): Doubly indexed dynamical systems: State space models and structural properties. - Math. Syst. Theory, Vol. 12. Zbl0392.93034
  5. Kaczorek T. (1988): Singular general model of 2D systems and its solution. - IEEE Trans. Automat. Contr., Vol. AC-33, No. 11, pp. 1060-1061. Zbl0655.93046
  6. Kaczorek T. (1993): Linear Control Systems, Vol. 1 and 2. - New York: Wiley. Zbl0784.93003
  7. Kaczorek T. (2001): Perfect observers for singular 2D linear systems. - Bull. Pol. Acad. Techn. Sci., Vol. 49, No. 1, pp. 141-147. Zbl0983.93033
  8. Kurek J. (1985): The general state-space model for two-dimensional linear digital system. - IEEE Trans. Autom. Contr., Vol. AC-30, No. 6,pp. 600-602. Zbl0561.93034
  9. Roesser P. R. (1975): A discrete state-space model for linear image processing. - IEEE Trans. Automat. Contr., Vol. AC-20, No. 1, pp. 1-10. Zbl0304.68099

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