Exterior algebra and invariant spaces of implicit systems: The Grassmann representative approach

 Access to full text

 Full (PDF)

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. (1992) 
2. P. Bernhard, On singular implicit linear dynamical systems, SIAM J. Control Optim. 20 (1982), 612-633. (1982) Zbl0491.93004MR0667644
3. F. R. Gantmacher, Theory of Matrices. Vol. 2, Chelsea, New York 1959. (1959) 
4. W. H. Greub, Multilinear Algebra, Springer Verlag, New York 1967. (1967) Zbl0169.35302MR0224623
5. W. V. D. Hodge, P. D. Pedoe, Methods of Algebraic Geometry. Vol. 2, Cambridge University Press, Cambridge 1952. (1952) MR0048065
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. (1981) MR0607261
7. G. Kalogeropoulos, Matrix Pencils and Linear Systems Theory, Ph.D. Thesis, Control Eng. Centre, City University, London, October 1985. (1985) 
8. N. Karcanias, Matrix pencil approach to geometric system theory, Proc. IEE 126 (1979), 585-590. (1979) MR0536439
9. N. Karcanias, Notes on exterior algebra and representation of exterior maps, Control Eng. Centre, Research Report, 1982. (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. (1989) MR0774143
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. (1974) MR1031051
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. (1981) MR0735816
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. (1985) Zbl0585.93008MR0845597
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. (1989) Zbl0689.93016MR1015178
15. F. Lewis, A tutorial on the geometric analysis of linear time invariant implicit systems, Automatica 28 (1992), 1, 119-138. (1992) Zbl0745.93033MR1144115
16. J. J. Loiseau, Some geometric consideration about the Kronecker normal form, Internat. J. Control 42 (1985), 1141-1431. (1985) MR0818345
17. M. Malabre, More geometry about singular systems, In: Proc. 26th IEEE CDC, Los Angeles 1987. (1987) 
18. M. Marcus, Finite Dimensional Multilinear Algebra. Vol. 1, 2, Marcel Dekker, New York 1973. (1973) MR0352112
19. M. Marcus, H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston 1964. (1964) Zbl0126.02404MR0162808
20. K. Ozčaldiran, Control of Descriptor Systems, PhD. thesis, School of Electrical Eng., Georgia Institute of Technology 1985. (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. (1987) 
22. R. Westwick, Linear transformations of Grassmann spaces III, Linear and Multilinear Algebra 2 (1974), 257-268. (1974) MR0429961
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. (1981) Zbl0463.93020
24. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, Springer-Verlag, New York 1979. (1979) Zbl0424.93001MR0569358