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Title: A pencil approach to high gain feedback and generalized state space systems (English)
Author: Hinrichsen, Diederich
Author: O'Halloran, Joyce
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 31
Issue: 2
Year: 1995
Pages: 109-139
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Category: math
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MSC: 15A22
MSC: 93B10
MSC: 93B25
MSC: 93B52
MSC: 93C05
idZBL: Zbl 0862.93033
idMR: MR1334505
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Date available: 2009-09-24T18:54:00Z
Last updated: 2012-06-06
Stable URL: http://hdl.handle.net/10338.dmlcz/124423
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Reference: [1] P. Brunovský: A classification of linear controllable systems.Kybernetika 3 (1970), 173-187. MR 0284247
Reference: [2] J. D. Cobb: Controllability, observability, and duality in singular systems.IEEE Trans. Automat. Control AC-29 (1984), 1076-1082. MR 0771396
Reference: [3] C. DeConcini D. Eisenbud, C. Procesi: Young diagrams and determinantal varieties.Invent. Math. 56(1980), 129-165. MR 0558865
Reference: [4] E. R. Gantmacher: The Theory of Matrices. Volume 1 and 2.Chelsea, New York 1959.
Reference: [5] H. Gliising-Luerlien: A feedback canonical form for singular systems.Internat. J. Control 52 (1990), 347-376. MR 1061724
Reference: [6] H. Gliising-LuerBen: Gruppenaktionen in der Theorie singularer Systeme.Ph.D. Thesis, Institut fur Dynamische Systeme, Universitat Bremen, 1991.
Reference: [7] D. Hinrichsen, J. O'Halloran: A complete characterization of orbit closures of controllable singular systems under restricted system equivalence.SIAM J. Control Optim. 25 (1990), 602-623. Zbl 0701.93017, MR 1047426
Reference: [8] D. Hinrichsen, J. O'Halloran: The orbit closure problem for matrix pencils: Necessary conditions and an application to high gain feedback.In: New Trends in Systems Theory, Birkhauser 1991, pp. 388-392. Zbl 0736.93032, MR 1125128
Reference: [9] D. Hinrichsen, J. O'Halloran: Orbit closures of matrix pencils and system limits under high gain feedback.In: Proc. 29th IEEE Conference on Decision and Control, Honolulu 1990, pp. 55-60.
Reference: [10] D. Hinrichsen, J. O'Halloran: A note on the degeneration of systems under pencil equivalence.In: Proc. 30th IEEE Conference on Decision and Control, Brighton 1991, pp. 1431-1432.
Reference: [11] D. Hinrichsen, J. O'Halloran: Orbit closure of singular matrix pencils.J. Pure Appl. Algebra 81 (1992), 117-137.
Reference: [12] D. Hinrichsen, J. O'Halloran: A note on the orbit closure problem for the generalized feedback group.In: Systems and Networks: Mathematical Theory and Applications, Vol. II - Invited and Contributed Papers, Akademie-Verlag, Berlin 1994, pp. 221-224. Zbl 0925.93401
Reference: [13] R. E. Kalman: Kronecker invariants and feedback.In: Ordinary Differential Equations, Proc. Conf. Ordinary Differential Equations (Weiss, ed.), Washington 1971. MR 0421751
Reference: [14] L. Kronecker: Algebraische Reduktion der Schaaren bilinearer Formen.S.-B. Akad. (1890), pp. 763-776.
Reference: [15] V. Kučera, P. Zagalak: Fundamental theorem of state feedback for singular systems.Automatica 24 (1988), 653-658. MR 0966689
Reference: [16] F. L. Lewis, K. Ozcaldiran: Reachability and controllability for descriptor systems.In: Proceedings of the 27th Midwestern Symposium on Circuits and Systems, Morgantown, West Virginia 1984, pp. 690-695.
Reference: [17] J. J. Loiseau K. Ozcaldiran M. Malabre, N. Karcanias: Feedback canonical forms of singular systems.Kybernetika 27 (1991), 289-305. MR 1127906
Reference: [18] J. O'Halloran: Feedback equivalence of constant linear systems.Systems Control Lett. 5 (1987), 241-246. Zbl 0628.93007, MR 0877091
Reference: [19] K. Ozcaldiran, F. L. Lewis: On the regularizability of singular systems.IEEE Trans. Automat. Control 50 (1990), 1156-1160. MR 1073262
Reference: [20] A. C. Pugh G. E. Hay ton, P. Fretwell: Transformation of matrix pencils and implications in linear systems theory.Internat. J. Control 45 (1987), 529-548. MR 0875557
Reference: [21] H. H. Rosenbrock: State Space and Multivariable Theory.Nelson-Wiley, New York 1970. Zbl 0246.93010, MR 0325201
Reference: [22] H. H. Rosenbrock: Structural properties of linear dynamical systems.Internat. J. Control 20 (1974), 177-189. Zbl 0285.93019, MR 0424303
Reference: [23] G.C. Verghese B. C. Levy, T. Kailath: A generalized state-space for singular systems.IEEE Trans. Automat. Control AC-26 (1981), 811-830. MR 0635842
Reference: [24] K. Weierstrass: Zur Theorie der bilinearen und quadratischen Formen.Monatsh. Akad. Wiss. (1867), 310-338.
Reference: [25] J. C. Willems: Paradigms and puzzles in the theory of dynamical systems.IEEE Trans. Automat. Control 56 (1991), 259-294. Zbl 0737.93004, MR 1092818
Reference: [26] W. M. Wonham: Linear Multivariable Control: A Geometric Approach.Second edition. Springer-Verlag, Heidelberg 1979. Zbl 0424.93001, MR 0569358
Reference: [27] E. L. Yip, R. F. Sincovic: Solvability, controllability, and observability of continuous descriptor systems.IEEE Trans. Automat. Control AC-26 (1981), 702-707. MR 0630799
Reference: [28] K. D. Young P. V. Kokotovic, and V.I. Utkin: A singular perturbation analysis of high-gain feedback systems.IEEE Trans. Automat. Control AC-22 (1977), 931-937. MR 0476055
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