Geodesic
Exterior algebra and invariant spaces of implicit systems: The Grassmann representative approach
Kybernetika, Tome 30 (1994) no. 1, pp. 1-22 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 93B25, 93C05 
@article{KYB_1994_30_1_a0,
     author = {Karcanias, Nicos and Baser, Ulviye},
     title = {Exterior algebra and invariant spaces of implicit systems: {The} {Grassmann} representative approach},
     journal = {Kybernetika},
     pages = {1--22},
     year = {1994},
     volume = {30},
     number = {1},
     mrnumber = {1267469},
     zbl = {0801.93021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1994_30_1_a0/}
}
TY  - JOUR
AU  - Karcanias, Nicos
AU  - Baser, Ulviye
TI  - Exterior algebra and invariant spaces of implicit systems: The Grassmann representative approach
JO  - Kybernetika
PY  - 1994
SP  - 1
EP  - 22
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_1994_30_1_a0/
LA  - en
ID  - KYB_1994_30_1_a0
ER  - 
%0 Journal Article
%A Karcanias, Nicos
%A Baser, Ulviye
%T Exterior algebra and invariant spaces of implicit systems: The Grassmann representative approach
%J Kybernetika
%D 1994
%P 1-22
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_1994_30_1_a0/
%G en
%F KYB_1994_30_1_a0
Karcanias, Nicos; Baser, Ulviye. Exterior algebra and invariant spaces of implicit systems: The Grassmann representative approach. Kybernetika, Tome 30 (1994) no. 1, pp. 1-22. http://geodesic.mathdoc.fr/item/KYB_1994_30_1_a0/

[1] U. Baser, N. Karcanias: An exterior algebra based characterisation of the fundamental subspaces of singular systems. In: Proceedings of 2nd IFAC Workshop on Systems Structure and Control, 1992, Prague, pp. 336-339.

[2] P. Bernhard: On singular implicit linear dynamical systems. SIAM J. Control Optim. 20 (1982), 612-633. | MR | Zbl

[3] F. R. Gantmacher: Theory of Matrices. Vol. 2. Chelsea, New York 1959.

[4] W. H. Greub: Multilinear Algebra. Springer Verlag, New York 1967. | MR | Zbl

[5] W. V. D. Hodge, P. D. Pedoe: Methods of Algebraic Geometry. Vol. 2. Cambridge University Press, Cambridge 1952. | MR

[6] S. Jaffe S., N. Karcanias: Matrix pencil characterization and almost $(A,B)$-invariant subspaces. A classification of geometric concepts. Internat. J. Control 33 (1981), 51-93. | MR

[7] G. Kalogeropoulos: Matrix Pencils and Linear Systems Theory. Ph.D. Thesis, Control Eng. Centre, City University, London, October 1985.

[8] N. Karcanias: Matrix pencil approach to geometric system theory. Proc. IEE 126 (1979), 585-590. | MR

[9] N. Karcanias: Notes on exterior algebra and representation of exterior maps. Control Eng. Centre, Research Report, 1982.

[10] N. Karcanias, C. Giannakopoulos: Grassmann invariants, almost zeros and the determinantal zero, pole assignment problems of linear systems. Internat. J. Control 40 (1989), 673-698. | MR

[11] N. Karcanias, C. Giannakopoulos: Grassmann matrices, decomposability of multivectors and the determinantal assignment problem. In: Linear Circuit Systems and Signal Processing: Theory and Applic. (C. I. Byrnes et al. eds.), North Holland 1974, pp. 307-312. | MR

[12] N. Karcanias, G. E. Hayton: Generalized autonomous dynamical systems, algebraic duality and geometric theory. In: Proc. IFAC VIII Triennial World Congress, Kyoto 1981, pp. 289-294. | MR

[13] N. Karcanias, G. Kalogeropoulos: Bilinear strict equivalence of matrix pencils. In: 4th IMA Int. Conference on Control Theory, Academic Press, Ed. P. A. Cook, 1985, pp. 77-86. | MR | Zbl

[14] N. Karcanias, G. Kalogeropoulos: Geometric theory and feedback invariants of generalized linear systems. A matrix pencil approach. Circuits Systems Signal Process. 8 (1989), 3, 375-397. | MR | Zbl

[15] F. Lewis: A tutorial on the geometric analysis of linear time invariant implicit systems. Automatica 28 (1992), 1, 119-138. | MR | Zbl

[16] J. J. Loiseau: Some geometric consideration about the Kronecker normal form. Internat. J. Control 42 (1985), 1141-1431. | MR

[17] M. Malabre: More geometry about singular systems. In: Proc. 26th IEEE CDC, Los Angeles 1987.

[18] M. Marcus: Finite Dimensional Multilinear Algebra. Vol. 1, 2. Marcel Dekker, New York 1973. | MR

[19] M. Marcus, H. Minc: A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston 1964. | MR | Zbl

[20] K. Ozčaldiran: Control of Descriptor Systems. PhD. thesis, School of Electrical Eng., Georgia Institute of Technology 1985.

[21] K. Ozčaldiran: A note on the assignment of initial and final manifolds for descriptor systems. In: Proc. of 1987 Intern. Symposium on Singular Systems, Atlanta, Georgia Tech 1987, pp. 38-39.

[22] R. Westwick: Linear transformations of Grassmann spaces III. Linear and Multilinear Algebra 2 (1974), 257-268. | MR

[23] J. C. Willems: Almost invariant subspaces: An approach to high gain feedback design. IEEE Trans Automat. Control AC-26 (1981), 235-252, AC-27 (1982), 1071-1085. | Zbl

[24] W. M. Wonham: Linear Multivariable Control: A Geometric Approach. Springer-Verlag, New York 1979. | MR | Zbl