Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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 ATPA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.
Rocznik
Tom
Strony
471--475
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Institute of Control and Industrial Electronics,Warsaw University of Technology, ul. Koszykowa 75, 00–662 Warsaw, Poland, kaczorek@isep.pw.edu.pl
Bibliografia
- [1] 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.
- [2] Bose N. K. (1985): Multidimensional Systems Theory Progress, Directions and Open Problems, Dordrecht: D. Reidel Publishing Co.
- [3] Farina L. and Rinaldi S. (2000): Positive Linear Systems. Theory and Applications. New York: Wiley.
- [4] Fornasini E. and Marchesini G. (1978): Double indexed dynamical systems. Mathematical Systems Theory, Vol. 12, pp. 59-72.
- [5] 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.
- [6] 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.
- [7] 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.
- [8] Gałkowski 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.
- [9] Kaczorek T. (1999): Externally positive 2D linear systems. Bulletin of the Polish Academy of Sciences: Technical Sciences, Vol. 47, No. 3, pp. 227-234.
- [10] Kaczorek T. (1996): Reachability and controllability of nonnegative 2D Roesser type models. Bulletin of the Polish Academy of Sciences: Technical Sciences, Vol. 44, No. 4, pp. 405-410.
- [11] Kaczorek T. (2000): Positive 1D and 2D Systems. London: Springer.
- [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.
- [13] Kaczorek T. (1985): Two-Dimensional Linear Systems. Berlin: Springer.
- [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.
- [16] Kurek J. (1985): The general state-space model for a twodimensional linear digital systems. IEEE Transactions on Automatic Control, Vol. -30, No. 2, pp. 600-602.
- [17] 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.
- [18] 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.
- [19] 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
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0041-0046