| Title:
|
Interpretations of the gap topology: A survey (English) |
| Author:
|
de Does, Jesse |
| Author:
|
Schumacher, J. M. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
30 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
105-120 |
| . |
| Category:
|
math |
| . |
| MSC:
|
93-02 |
| MSC:
|
93A30 |
| MSC:
|
93B25 |
| MSC:
|
93C05 |
| MSC:
|
93C99 |
| idZBL:
|
Zbl 0800.93740 |
| idMR:
|
MR1283488 |
| . |
| Date available:
|
2009-09-24T18:45:25Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125001 |
| . |
| Reference:
|
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| Reference:
|
[2] C. I. Byrnes, T. E. Duncan: On certain topological invariants arising in system theory.In: New Directions in Applied Mathematics, Springer, New York 1982, pp. 29-71. Zbl 0483.93049, MR 0661283 |
| Reference:
|
[3] J. de Does H. Glüsing-Lüerssen, J. M. Schumacher: Connectedness properties of spaces of linear systems.In: Proc. SINS '92 International Symposium on Implicit and Nonlinear Systems (Ft. Worth, Texas, Dec. 14-15, 1992), (F. L. Lewis, ed.), ARRI, Univ. Texas at Arlington, pp. 210-215. |
| Reference:
|
[4] I. C. Gohberg, M. G. Krein: Introduction to the Theory of Linear Nonselfadjoint Operators.Transl. Math. Monogr. 18, Amer. Math. Soc, Providence, RI 1969. Zbl 0181.13504, MR 0246142 |
| Reference:
|
[5] C. Foias T. T. Georgiou, M. C. Smith: Robust stabilization in the gap metric: a geometric approach.Proc. 1991 International Symposium on the Mathematical Theory of Networks and Systems, Kobe, Japan, June 1991. MR 1197941 |
| Reference:
|
[6] C. Martin, R. Hermann: Applications of algebraic geometry to systems theory: The McMillan degree and Kronecker indices of transfer functions as topological and holomorphic system invariants.SIAM J. Control Optim. 16 (1978), 743-755. Zbl 0401.93020, MR 0527294 |
| Reference:
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[7] T. Kato: Perturbation Theory for Linear Operators.Springer, New York 1982. Zbl 0493.47008 |
| Reference:
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[8] P. D. Lax: Translation invariant subspaces.Acta Math. 101 (1959), 163-178. MR 0105620 |
| Reference:
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[9] N. K. Nikol'skiĭ: Treatise on the Shift Operator.Springer, Berlin 1986. MR 0827223 |
| Reference:
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[10] R. J. Ober, J. A. Sefton: Stability of control systems and graphs of linear systems.Systems Control Lett. 17 (1991), 265-280. Zbl 0747.93062, MR 1129217 |
| Reference:
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[11] L. Qiu, E. J. Davison: Pointwise gap metrics on transfer matrices.IEEE Trans. Automat. Control 37 (1992), 741-758. Zbl 0755.93067, MR 1164546 |
| Reference:
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[12] L. Qiu, E. J. Davison: Feedback stability under simultaneous gap metric uncertainties in plant and controller.Systems Control Lett. 18 (1992), 9-22. Zbl 0743.93083, MR 1146910 |
| Reference:
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[13] J. M. Schumacher: A pointwise criterion for controller robustness.Systems Control Lett. 18 (1992), 1-8. Zbl 0743.93080, MR 1146909 |
| Reference:
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[14] M. Vidyasagar: Control System Synthesis: a Factorization Approach.MIT Press, Cambridge, MA 1985. Zbl 0655.93001, MR 0787045 |
| Reference:
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[15] S. Weiland: Theory of Approximation and Disturbance Attenuation for Linear Systems.Doctoral Dissertation, University of Groningen 1991. |
| Reference:
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[16] J. C. Willems: Input-output and state-space representations of finite-dimensional linear time-invariant systems.Linear Algebra Appl. 50 (1983), 581-608. Zbl 0507.93017, MR 0699576 |
| Reference:
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[17] J. C. Willems: Paradigms and puzzles in the theory of dynamical systems.IEEE Trans. Automat. Control 36 (1991), 259-294. Zbl 0737.93004, MR 1092818 |
| Reference:
|
[18] G. Zames, A. K. El-Sakkary: Unstable systems and feedback: The gap metric.In: Proc. Allerton Conf. (1980), pp. 380-385. |
| Reference:
|
[19] S. Q. Zhu: Graph topology and gap topology for unstable systems.IEEE Trans. Automat. Control 34 (1989), 848-855. Zbl 0697.93030, MR 1004302 |
| . |
