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2007 | 17 | 4 | 471-475
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
17
Numer
4
Strony
471-475
Opis fizyczny
Daty
wydano
2007
(nieznana)
2006-12-15
otrzymano
2007-06-25
poprawiono
2007-07-30
Twórcy
  • Institute of Control and Industrial Electronics, Warsaw University of Technology, ul. Koszykowa75, 00-0663 Warsaw, Poland
Bibliografia
  • Benvenuti L. and Farina L. (2004): A tutorial on the positive realization problem. IEEE Transactions on Automatic Control, Vol.49, No.5, pp.651-664.
  • Bose N. K. (1985): Multidimensional Systems Theory Progress, Directions and Open Problems, Dordrecht: D. Reidel Publishing Co.
  • Farina L. and Rinaldi S. (2000): Positive Linear Systems. Theory and Applications. New York: Wiley.
  • Fornasini E. and Marchesini G. (1978): Double indexed dynamical systems. Mathematical Systems Theory, Vol.12, pp.59-72.
  • Fornasini E. and Marchesini G. (1976): State-space realization theory of two- dimensional filters. IEEE Transactions on Automatic Control, Vol.AC-21, pp.484-491.
  • Fornasini E. and Valcher M.E. (1996): On the spectral and combinatorial structure of 2D positive systems. Linear Algebra and Its Applications, Vol.245, pp.223-258.
  • Fornasini E. and Valcher M.E. (1997): Recent developments in 2D positive systems theory. International Journal of Applied Mathematics and Computer Science, Vol.7, No.4, pp.101-123.
  • Galkowski K. (1997): Elementary operation approach to state space realization of 2D systems. IEEE Transaction on Circuits and Systems, Vol.44, No.2, pp.120-129.
  • Kaczorek T. (1999): Externally positive 2D linear systems. Bulletin of the Polish Academy of Sciences: Technical Sciences, Vol.47, No.3, pp.227-234.
  • Kaczorek T. (1996): Reachability and controllability of non-negative 2D Roesser type models. Bulletin of the Polish Academy of Sciences: Technical Sciences, Vol.44, No.4, pp.405-410.
  • Kaczorek T. (2000): Positive 1D and 2D Systems. London: Springer.
  • 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.
  • Kaczorek T. (1985): Two-Dimensional Linear Systems. Berlin: Springer.
  • 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.
  • Klamka J. (1991): Controllability of dynamical systems. Dordrecht: Kluwer.
  • 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.
  • Kurek J. (2002): Stability of positive 2D systems described by the Roesser model. IEEE Transactions on Circuits and Systems I, Vol.49, No.4, pp.531-533.
  • Roesser R.P. (1975) A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, Vol.AC-20, No.1, pp.1-10.
  • Valcher M.E. and Fornasini E. (1995): State models and asymptotic behaviour of 2D Roesser model. IMA Journal on Mathematical Control and Information, No.12, pp.17-36
Typ dokumentu
Bibliografia
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