The controllability and reconstructability (global) of the system described by a digital N-D Roesser model are defined. Then, necessary and sufficient conditions for system controllability and reconstructability are given. The conditions constitute a generalization of the corresponding conditions for 1-D systems.
@article{bwmeta1.element.bwnjournal-article-amcv13i1p55bwm,
author = {Kurek, Jerzy},
title = {Controllability and reconstructability of a system described by the N-D Roesser model},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {13},
year = {2003},
pages = {55-60},
zbl = {1046.93032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv13i1p55bwm}
}
Kurek, Jerzy. Controllability and reconstructability of a system described by the N-D Roesser model. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) pp. 55-60. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv13i1p55bwm/
[000] Attasi S. (1973): Systemes lineaires homogénes á deux indices. - Rapport Laboria, Vol. 31, No. 1, pp. 1-37.
[001] Bisiacco M. (1985): State and output feedback stabilizability of 2-D systems. - IEEE Trans. Circ. Syst., Vol. CAS-32, No. 11, pp. 1246-1254. | Zbl 0583.93047
[002] Fornasini E. and Marchesini G. (1978): Doubly indexed dynamical systems: State-space models and structural properties. - Math. Syst. Theory, Vol. 12, No. 1, pp. 59-72. | Zbl 0392.93034
[003] Kaczorek T. (1985): Two-Dimensional Linear Systems. - Heidelberg: Springer. | Zbl 0593.93031
[004] Kung S.Y., Levy B.C., Morf M. and Kailath T. (1977): New results in 2-D systems theory, Part II: 2-D state-space model realization and the notionsof controllability, observability, and minimality. - Proc. IEEE, Vol. 65, No. 10, pp. 945-961.
[005] Kurek J.E. (1985): The general state-space model for a two-dimensional linear digital systems. - IEEE Trans. Automat. Contr., Vol. AC-30, No. 5, pp. 600-602. | Zbl 0561.93034
[006] Kurek J.E. (1987): Observability and reconstructability of 2-D linear digital systems. - IEEE Trans. Automat. Contr., Vol. AC-32, No. 2, pp. 170-172. | Zbl 0606.93019
[007] Kurek J.E. (1987): Reachability of a system described by the multidimensional Roesser model. - Int. J. Contr., Vol. 45, No. 6, pp. 1559-1563. | Zbl 0622.93008
[008] Kurek J.E. (1990): Controllability of the 2-D Roesser model. - Multidim. Syst. Signal Process., Vol. 1, No. 5, pp. 381-387. | Zbl 0725.93012
[009] Kurek J.E. (1990): Genericness of solution to N-dimensional polynomial matrix equation XA=I. - IEEE Trans Circ. Syst., Vol. 37, No. 9, pp. 1041-1043. | Zbl 0708.15005
[010] Marszalek W. (1984): Two dimensional state-space discrete models for hyperbolic partial differential equations. - Appl. Math. Models, Vol. 8, No. 1, pp. 11-14. | Zbl 0529.65039
[011] Roesser R.P. (1975): A discrete state-space model for linear imageprocessing. - IEEE Trans. Automat. Contr., Vol. AC-20, No. 1, pp. 1-10. | Zbl 0304.68099
[012] Youla D.C. (1979): Notes on N-dimensional system theory. - IEEE Trans. Circuits Sys., Vol. CAS-26, No. 1, pp. 105-111. | Zbl 0394.93004