| Title:
|
Exterior algebra and invariant spaces of implicit systems: The Grassmann representative approach (English) |
| Author:
|
Karcanias, Nicos |
| Author:
|
Baser, Ulviye |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
30 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
1-22 |
| . |
| Category:
|
math |
| . |
| MSC:
|
93B25 |
| MSC:
|
93C05 |
| idZBL:
|
Zbl 0801.93021 |
| idMR:
|
MR1267469 |
| . |
| Date available:
|
2009-09-24T18:44:34Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124501 |
| . |
| Reference:
|
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| Reference:
|
[2] P. Bernhard: On singular implicit linear dynamical systems.SIAM J. Control Optim. 20 (1982), 612-633. Zbl 0491.93004, MR 0667644 |
| Reference:
|
[3] F. R. Gantmacher: Theory of Matrices. Vol. 2.Chelsea, New York 1959. |
| Reference:
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[4] W. H. Greub: Multilinear Algebra.Springer Verlag, New York 1967. Zbl 0169.35302, MR 0224623 |
| Reference:
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[5] W. V. D. Hodge, P. D. Pedoe: Methods of Algebraic Geometry. Vol. 2.Cambridge University Press, Cambridge 1952. MR 0048065 |
| Reference:
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[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 0607261 |
| Reference:
|
[7] G. Kalogeropoulos: Matrix Pencils and Linear Systems Theory.Ph.D. Thesis, Control Eng. Centre, City University, London, October 1985. |
| Reference:
|
[8] N. Karcanias: Matrix pencil approach to geometric system theory.Proc. IEE 126 (1979), 585-590. MR 0536439 |
| Reference:
|
[9] N. Karcanias: Notes on exterior algebra and representation of exterior maps.Control Eng. Centre, Research Report, 1982. |
| Reference:
|
[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 0774143 |
| Reference:
|
[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 1031051 |
| Reference:
|
[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 0735816 |
| Reference:
|
[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. Zbl 0585.93008, MR 0845597 |
| Reference:
|
[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. Zbl 0689.93016, MR 1015178 |
| Reference:
|
[15] F. Lewis: A tutorial on the geometric analysis of linear time invariant implicit systems.Automatica 28 (1992), 1, 119-138. Zbl 0745.93033, MR 1144115 |
| Reference:
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[16] J. J. Loiseau: Some geometric consideration about the Kronecker normal form.Internat. J. Control 42 (1985), 1141-1431. MR 0818345 |
| Reference:
|
[17] M. Malabre: More geometry about singular systems.In: Proc. 26th IEEE CDC, Los Angeles 1987. |
| Reference:
|
[18] M. Marcus: Finite Dimensional Multilinear Algebra. Vol. 1, 2.Marcel Dekker, New York 1973. MR 0352112 |
| Reference:
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[19] M. Marcus, H. Minc: A Survey of Matrix Theory and Matrix Inequalities.Allyn and Bacon, Boston 1964. Zbl 0126.02404, MR 0162808 |
| Reference:
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[20] K. Ozčaldiran: Control of Descriptor Systems.PhD. thesis, School of Electrical Eng., Georgia Institute of Technology 1985. |
| Reference:
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[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. |
| Reference:
|
[22] R. Westwick: Linear transformations of Grassmann spaces III.Linear and Multilinear Algebra 2 (1974), 257-268. MR 0429961 |
| Reference:
|
[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 0463.93020 |
| Reference:
|
[24] W. M. Wonham: Linear Multivariable Control: A Geometric Approach.Springer-Verlag, New York 1979. Zbl 0424.93001, MR 0569358 |
| . |
