A pencil approach to high gain feedback and generalized state space systems

Diederich Hinrichsen; Joyce O'Halloran

Kybernetika (1995)

  • Volume: 31, Issue: 2, page 109-139
  • ISSN: 0023-5954

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Hinrichsen, Diederich, and O'Halloran, Joyce. "A pencil approach to high gain feedback and generalized state space systems." Kybernetika 31.2 (1995): 109-139. <http://eudml.org/doc/27578>.

@article{Hinrichsen1995,
author = {Hinrichsen, Diederich, O'Halloran, Joyce},
journal = {Kybernetika},
keywords = {linear systems; generalized state space systems; high-gain feedback; feedback equivalence; singular matrix pencils; feedback groups},
language = {eng},
number = {2},
pages = {109-139},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A pencil approach to high gain feedback and generalized state space systems},
url = {http://eudml.org/doc/27578},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Hinrichsen, Diederich
AU - O'Halloran, Joyce
TI - A pencil approach to high gain feedback and generalized state space systems
JO - Kybernetika
PY - 1995
PB - Institute of Information Theory and Automation AS CR
VL - 31
IS - 2
SP - 109
EP - 139
LA - eng
KW - linear systems; generalized state space systems; high-gain feedback; feedback equivalence; singular matrix pencils; feedback groups
UR - http://eudml.org/doc/27578
ER -

References

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  1. P. Brunovský, A classification of linear controllable systems, Kybernetika 3 (1970), 173-187. (1970) MR0284247
  2. J. D. Cobb, Controllability, observability, and duality in singular systems, IEEE Trans. Automat. Control AC-29 (1984), 1076-1082. (1984) MR0771396
  3. C. DeConcini D. Eisenbud, C. Procesi, Young diagrams and determinantal varieties, Invent. Math. 56(1980), 129-165. (1980) MR0558865
  4. E. R. Gantmacher, The Theory of Matrices. Volume 1 and 2, Chelsea, New York 1959. (1959) 
  5. H. Gliising-Luerlien, A feedback canonical form for singular systems, Internat. J. Control 52 (1990), 347-376. (1990) MR1061724
  6. H. Gliising-LuerBen, Gruppenaktionen in der Theorie singularer Systeme, Ph.D. Thesis, Institut fur Dynamische Systeme, Universitat Bremen, 1991. (1991) 
  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. (1990) Zbl0701.93017MR1047426
  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. (1991) Zbl0736.93032MR1125128
  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. (1990) 
  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. (1991) 
  11. D. Hinrichsen, J. O'Halloran, Orbit closure of singular matrix pencils, J. Pure Appl. Algebra 81 (1992), 117-137. (1992) 
  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. (1994) Zbl0925.93401
  13. R. E. Kalman, Kronecker invariants and feedback, In: Ordinary Differential Equations, Proc. Conf. Ordinary Differential Equations (Weiss, ed.), Washington 1971. (1971) MR0421751
  14. L. Kronecker, Algebraische Reduktion der Schaaren bilinearer Formen, S.-B. Akad. (1890), pp. 763-776. 
  15. V. Kučera, P. Zagalak, Fundamental theorem of state feedback for singular systems, Automatica 24 (1988), 653-658. (1988) MR0966689
  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. (1984) 
  17. J. J. Loiseau K. Ozcaldiran M. Malabre, N. Karcanias, Feedback canonical forms of singular systems, Kybernetika 27 (1991), 289-305. (1991) MR1127906
  18. J. O'Halloran, Feedback equivalence of constant linear systems, Systems Control Lett. 5 (1987), 241-246. (1987) Zbl0628.93007MR0877091
  19. K. Ozcaldiran, F. L. Lewis, On the regularizability of singular systems, IEEE Trans. Automat. Control 50 (1990), 1156-1160. (1990) MR1073262
  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. (1987) MR0875557
  21. H. H. Rosenbrock, State Space and Multivariable Theory, Nelson-Wiley, New York 1970. (1970) Zbl0246.93010MR0325201
  22. H. H. Rosenbrock, Structural properties of linear dynamical systems, Internat. J. Control 20 (1974), 177-189. (1974) Zbl0285.93019MR0424303
  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. (1981) MR0635842
  24. K. Weierstrass, Zur Theorie der bilinearen und quadratischen Formen, Monatsh. Akad. Wiss. (1867), 310-338. 
  25. J. C. Willems, Paradigms and puzzles in the theory of dynamical systems, IEEE Trans. Automat. Control 56 (1991), 259-294. (1991) Zbl0737.93004MR1092818
  26. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, Second edition. Springer-Verlag, Heidelberg 1979. (1979) Zbl0424.93001MR0569358
  27. E. L. Yip, R. F. Sincovic, Solvability, controllability, and observability of continuous descriptor systems, IEEE Trans. Automat. Control AC-26 (1981), 702-707. (1981) MR0630799
  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. (1977) MR0476055

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