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The choice of the forms of Lyapunov functions for a positive 2D Roesser model

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 4, page 471-475
  • ISSN: 1641-876X

Abstract

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The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix A^{T}PA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.

How to cite

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Kaczorek, Tadeusz. "The choice of the forms of Lyapunov functions for a positive 2D Roesser model." International Journal of Applied Mathematics and Computer Science 17.4 (2007): 471-475. <http://eudml.org/doc/207852>.

@article{Kaczorek2007,
abstract = {The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix A^\{T\}PA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {asymptotic stability; positive 2D Roesser model; Lyapunov function},
language = {eng},
number = {4},
pages = {471-475},
title = {The choice of the forms of Lyapunov functions for a positive 2D Roesser model},
url = {http://eudml.org/doc/207852},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - The choice of the forms of Lyapunov functions for a positive 2D Roesser model
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 4
SP - 471
EP - 475
AB - The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix A^{T}PA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.
LA - eng
KW - asymptotic stability; positive 2D Roesser model; Lyapunov function
UR - http://eudml.org/doc/207852
ER -

References

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  11. Kaczorek T. (2000): Positive 1D and 2D Systems. London: Springer. Zbl0978.93003
  12. Kaczorek T. (2002): When the equilibrium of positive 2D Roesser model are strictly positive. Bulletin of the Polish Academy of Sciences: Technical Sciences, Vol.50, No.3, pp.221-227. Zbl1138.93319
  13. Kaczorek T. (1985): Two-Dimensional Linear Systems. Berlin: Springer. Zbl0593.93031
  14. Klamka J. (1999): Controllability of 2D linear systems, In: Advances in Control Highlights of ECC 1999 (P.M. Frank, Ed.), Berlin: Springer, pp.319-326. 
  15. Klamka J. (1991): Controllability of dynamical systems. Dordrecht: Kluwer. Zbl0732.93008
  16. Kurek J. (1985): The general state-space model for a two-dimensional linear digital systems. IEEE Transactions on Automatic Control, Vol.-30, No.2, pp.600-602. Zbl0561.93034
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