Geodesic
An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring
Kybernetika, Tome 35 (1999) no. 6, pp. 765-776 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The paper presents procedures to check solvability and to compute solutions to the Block Decoupling Problem over a Noetherian ring and procedures to compute a feedback law that assigns the coefficients of the compensated system while mantaining the decoupled structure over a Principal Ideal Domain. The algorithms have been implemented using MapleV® and CoCoA [CoCoA].
The paper presents procedures to check solvability and to compute solutions to the Block Decoupling Problem over a Noetherian ring and procedures to compute a feedback law that assigns the coefficients of the compensated system while mantaining the decoupled structure over a Principal Ideal Domain. The algorithms have been implemented using MapleV® and CoCoA [CoCoA].
Classification : 93-04, 93B25, 93B40, 93B51
Keywords: block decoupling problem over a Noetherian ring; feedback law; principal ideal domain 
@article{KYB_1999_35_6_a8,
     author = {Assan, Jean and Perdon, Anna M.},
     title = {An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring},
     journal = {Kybernetika},
     pages = {765--776},
     year = {1999},
     volume = {35},
     number = {6},
     mrnumber = {1747975},
     zbl = {1274.93087},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_6_a8/}
}
TY  - JOUR
AU  - Assan, Jean
AU  - Perdon, Anna M.
TI  - An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring
JO  - Kybernetika
PY  - 1999
SP  - 765
EP  - 776
VL  - 35
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_1999_35_6_a8/
LA  - en
ID  - KYB_1999_35_6_a8
ER  - 
%0 Journal Article
%A Assan, Jean
%A Perdon, Anna M.
%T An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring
%J Kybernetika
%D 1999
%P 765-776
%V 35
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_1999_35_6_a8/
%G en
%F KYB_1999_35_6_a8
Assan, Jean; Perdon, Anna M. An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring. Kybernetika, Tome 35 (1999) no. 6, pp. 765-776. http://geodesic.mathdoc.fr/item/KYB_1999_35_6_a8/

[1] Adams W. W., Loustaunau P.: An introduction to Gröbner bases. (Graduate Studies in Mathematics 3.) Amer. Math. Soc. 1996 | MR | Zbl

[2] Assan J., Lafay J. F., Perdon A. M.: An algorithm to compute maximal pre–controllability submodules over a Principal Ideal Domain. In: Proc. IFAC Workshop on Linear Time Delay Systems, Grenoble 1998, pp. 123–128

[3] Assan J., Lafay J. F., Perdon A. M.: Computation of maximal pre-controllability submodules over a Noetherian ring (to appear.

[4] Basile G., Marro G.: Controlled and Conditioned Invariants in Linear System Theory. Prentice Hall, Englewood Cliffs, N. J. 1992 | MR | Zbl

[5] Brewer J. W., Klinger L. C., Schmale W.: The dynamic feedback cyclization problem for Principal Ideal Domains. J. Pure Appl. Algebra (1994), 31–42

[6] Buchberger B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph.D. Thesis, University of Innsbruck, Innsbruck 1965

[8] Conte G., Perdon A. M.: The disturbance decoupling problem for systems over a ring. SIAM J. Control Optim. 33 (1995), 3, 750–764 | DOI | MR | Zbl

[9] Conte G., Perdon A. M.: The block decoupling problem for systems over a ring. IEEE Trans. Automat. Control 43 (1998), 11, 1600–1604 | DOI | MR | Zbl

[10] Conte G., Perdon A. M., Lombardo A.: Block decoupling problem with coefficient assignment and stability for linear systems over Noetherian rings. In: Proc. IFAC Conference on System Structure and Control, Nantes 1998

[11] Emre E., Khargonekar P.: Regulation of split linear systems over rings; coefficient assignment and observers. IEEE Trans. Automat. Control AC–27 (1982), 1, 104–113 | DOI | MR | Zbl

[12] Dübbelde J., Schmale W.: Normalformproblem und Koefficientenzuweisung bei Systemen über euklidischen Ringen. University of Oldenburg, 1994

[13] Hautus M. L. J.: Disturbance rejection for systems over rings. (Lecture Notes in Control and Infomation Sciences 58.) Springer–Verlag, Berlin 1984 | DOI | MR | Zbl

[14] Inaba H., Ito N., Munaka T.: Decoupling and pole assignment for linear systems defined over a Principal Ideal Domain. In: Linear Circuits, Systems and Signal Processing: Theory and Applications (C. I. Byrnes, C. F. Martin, R. E. Saeks, eds.), North Holland, Amsterdam 1988 | MR

[15] Lang S.: Algebra. Second edition. Addison Wesley, Reading 1984 | MR | Zbl

[16] Sename O., Lafay J. F.: Decoupling of square linear systems with delays. IEEE Trans. Automat. Control 42 (1997), 5, 736–742 | DOI | MR | Zbl

[17] Wonham M.: Linear Multivariable Control: A Geometric Approach. Third edition. Springer–Verlag, New York 1985 | MR | Zbl