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.
@article{bwmeta1.element.bwnjournal-article-amcv11i2p369bwm, author = {Kaczorek, Tadeusz}, title = {Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {11}, year = {2001}, pages = {369-376}, zbl = {0982.93047}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i2p369bwm} }
Kaczorek, Tadeusz. Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 369-376. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i2p369bwm/
[000] Dai L. (1988): Observers for discrete singular systems. - IEEE Trans. Automat. Contr., Vol. AC-33, No. 2, pp. 187-191. | Zbl 0633.93025
[001] Dai L. (1989): Singular Control Systems. - Berlin, Tokyo: Springer. | Zbl 0669.93034
[002] 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. | Zbl 0332.93072
[003] Fornasini E. and Marchesini G. (1978): Doubly indexed dynamical systems: State space models and structural properties. - Math. Syst. Theory, Vol. 12. | Zbl 0392.93034
[004] Kaczorek T. (1988): Singular general model of 2D systems and its solution. - IEEE Trans. Automat. Contr., Vol. AC-33, No. 11, pp. 1060-1061. | Zbl 0655.93046
[005] Kaczorek T. (1993): Linear Control Systems, Vol. 1 and 2. - New York: Wiley. | Zbl 0784.93003
[006] Kaczorek T. (2001): Perfect observers for singular 2D linear systems. - Bull. Pol. Acad. Techn. Sci., Vol. 49, No. 1, pp. 141-147. | Zbl 0983.93033
[007] 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. | Zbl 0561.93034
[008] 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. | Zbl 0304.68099