@article{KYB_1995_31_6_a1,
author = {Eliopoulou, Helen and Karcanias, Nicos},
title = {Properties of reachability and almost reachability subspaces of implicit systems: {The} extension problem},
journal = {Kybernetika},
pages = {530--540},
year = {1995},
volume = {31},
number = {6},
mrnumber = {1374142},
zbl = {0864.93022},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_1995_31_6_a1/}
}
TY - JOUR AU - Eliopoulou, Helen AU - Karcanias, Nicos TI - Properties of reachability and almost reachability subspaces of implicit systems: The extension problem JO - Kybernetika PY - 1995 SP - 530 EP - 540 VL - 31 IS - 6 UR - http://geodesic.mathdoc.fr/item/KYB_1995_31_6_a1/ LA - en ID - KYB_1995_31_6_a1 ER -
Eliopoulou, Helen; Karcanias, Nicos. Properties of reachability and almost reachability subspaces of implicit systems: The extension problem. Kybernetika, Tome 31 (1995) no. 6, pp. 530-540. http://geodesic.mathdoc.fr/item/KYB_1995_31_6_a1/
[1] D. J. Aplevich: Minimal representation of implicit linear systems. Automatica 21 (1985), 259-269. | MR
[2] D. Bernard: On singular implicit linear dynamical systems. SIAM J. Control Optim. 29 (1989), 612-633. | MR
[3] H. Eliopoulou: A Matrix Pencil Approach for the Study of Geometry and Feedback Invariants of Singular Systems. PhD Thesis, Control Eng. Centre, City University, London 1994.
[4] H. Eliopoulou, N. Karcanias: Geometric properties of the singular Segre characteristic at infinity of a pencil. In: Recent Advances in Mathematical Theory of Systems, Control Networks and Signal Processing II - Proceedings of the International Symposium MTNS 91, Tokyo, pp. 109-114. | MR
[5] H. Eliopoulou, N. Karcanias: Toeplitz matrix characterisation and computation of the fundamental subspaces of singular systems. In: Proceedings of Symposium of Implicit and Nonlinear Systems SINS'92, The Aut. & Robotics Res. Inst., University of Texas at Arlington 1992, pp. 216-221.
[6] H. Eliopoulou, N. Karcanias: On the study of the chains and spaces related to the Kronecker invariants via their generators. Part II: Elementary divisors. (submitted for publication).
[7] F. R. Gantmacher: Theory of Matrices. Chelsea, New York 1959. | Zbl
[8] S. Jaffe, N. Karcanias: Matrix pencil characterisation of almost (A, B) invariant subspaces: A classification of geometric concepts. Internat. J. Control 33 (1981), 51-93. | MR
[9] G. Kalogeropoulos: Matrix Pencils and Linear System Theory. PhD Thesis, Control Eng. Centre, City University, London 1985.
[10] N. Karcanias: Proper invariant realisation of singular system problems. IEEE Trans. Automat. Control AC-35 (1990), 2, 230-233. | MR
[11] N. Karcanias: Minimal bases of matrix pencils: Algebraic, Toeplitz structure and geometric properties. Linear Algebra Appl. 205-206 (1994), 205-206. | MR | Zbl
[12] N. Karcanias: The selection of input and output schemes for a system and the model projection problems. Kybernetika 30 (1994), 585-596. | MR | Zbl
[13] N. Karcanias, G. Kalogeropoulos: Geometric theory and feedback invariants of generalised linear systems: A matrix pencil approach. Circuits Systems Signal Process. 8 (1989), 375-397. | MR
[14] N. Karcanias, H. Eliopoulou: On the study of the chains and spaces related to the Kronecker invariants via their generators. Part I: Minimal bases for matrix pencils. (submitted for publication).
[15] N. Karcanias, G. Hayton: Generalised autonomouc dynamical systems, algebraic duality and geometric theory. In: Proc. IFAC VIII Trennial World Congress, Kyoto 1981. | MR
[16] N. Karcanias, D. Vafiadis: On the cover problems of geometric theory. Kybernetika 29 (1993), 547-562. | MR | Zbl
[17] F. Lewis: A tutorial on the geometric analysis of linear time invariant implicit systems. Automatica 28 (1992), 119-138. | MR | Zbl
[18] J. J. Loiseau: Some geometric considerations about the Kronecker normal form. Internat. J. Control 42 (1985), 6, 1411-1431. | MR | Zbl
[19] K. Ozcaldiran: Control of Descriptor Systems. PhD Thesis, School of Elec. Eng., Georgia Institute of Techn., Atlanta 1985.
[20] K. Ozcaldiran: A geometric characterisation of reachable and controllable subspaces of descriptor systems. Circuits Systems Signal Process. 5 (1986), 1, 37-48. | MR
[21] K. Ozcaldiran, F. L. Lewis: Generalised reachability subspaces for singular systems. SIAM J. Control Optim. 26 (1989), 495-510. | MR
[22] H. L. Trentelman: Almost Invariant Subspaces and High Gain Feedback. PhD Thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology 1985. | 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. Second edition. Springer-Verlag, New York 1979. | MR | Zbl