Analysis of some dual properties in discrete dynamic systems
International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) no. 3, pp. 297-308.

Voir la notice de l'article provenant de la source Library of Science

The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.
Keywords: nonlinear system, linear system, algebraic approach, error correction, reachability, duality
Mots-clés : układ liniowy, układ nieliniowy, system dynamiczny, system dyskretny, dwoistość
@article{IJAMCS_2006_16_3_a1,
     author = {Zhirabok, A.},
     title = {Analysis of some dual properties in discrete dynamic systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {297--308},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_3_a1/}
}
TY  - JOUR
AU  - Zhirabok, A.
TI  - Analysis of some dual properties in discrete dynamic systems
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2006
SP  - 297
EP  - 308
VL  - 16
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_3_a1/
LA  - en
ID  - IJAMCS_2006_16_3_a1
ER  - 
%0 Journal Article
%A Zhirabok, A.
%T Analysis of some dual properties in discrete dynamic systems
%J International Journal of Applied Mathematics and Computer Science
%D 2006
%P 297-308
%V 16
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_3_a1/
%G en
%F IJAMCS_2006_16_3_a1
Zhirabok, A. Analysis of some dual properties in discrete dynamic systems. International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) no. 3, pp. 297-308. http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_3_a1/

[1] Arbib M. and Manes E. (1974): Foundation of system theory: Decomposable systems. - Automatica, Vol. 10, No. 2, pp. 285-302.

[2] Bellman R. (1960): Introduction to Matrix Analysis. - New York: McGraw-Hill Company, Inc.

[3] Gill A. (1971): Linear Sequential Circuits. Analysis, Synthesis, and Application. -New York: McGraw-Hill.

[4] Goldblad R. (1979): Topoi. The Categorical Analysis of Logic. -Amsterdam: North-Holland.

[5] Hermann R. and Krener A. (1977): Nonlinear controllability and observability. - IEEE Trans. Automat. Contr., Vol. AC-22, No. 5, pp. 728-740.

[6] Korn G.A. and Korn T.M. (1961): Mathematical Handbook. - New York: McGraw-Hill.

[7] Lankaster P. (1969): Theory of Matrices. -London: Academic Press.

[8] Kwakernaak H. and Sivan R. (1972): Linear Optimal Control Systems. -New York: Wiley.

[9] Michtchenko A. and Zhirabok A. (2001): Application of invariance for error correction in nonlinear systems. - Proc. 12-th Int. Symp. Danube Adria Association for Automation and Manufacturing, Vienna, Austria, pp. 297-298.

[10] Peterson W. and Weldon E. (1972): Error-Correcting Codes. -London: Mita Press.

[11] Shumsky A. and Zhirabok A. (2005): Nonlinear diagnostic filter design: Algebraic and geometric points of view. - Proc. 16-th IFAC World Congress, Prague, Czech Republic, (on CD-ROM).

[12] Zhirabok A. and Shumsky A. (1993): A new mathematical technique for nonlinear systems research. - Proc. 12-th IFAC World Congress, Sydney, Australia, Vol. 3, pp. 485-488.

[13] Zhirabok A. (1998): Observability and controllability properties of nonlinear dynamic systems.-Int. J. Comput. Syst. Sci., Vol. 37, No. 1, pp. 1-4.

[14] Zhirabok A. (2000): On canonical decomposition of nonlinear dynamic systems, In: Nonlinear Control in the Year 2000, Vol. 2, (F. Lamnabhi-Lagarrigue, A. Isidori, W. Respondek, Eds.).-London: Springer, pp. 555-564.