| Title:
|
The technique of splitting operators in perturbation control theory (English) |
| Author:
|
Konstantinov, Mihail M. |
| Author:
|
Petkov, Petko Hr. |
| Author:
|
Christov, Nicolai D. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
[15]-32 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper presents the technique of splitting operators, intended for perturbation analysis of control problems involving unitary matrices. Combined with the technique of Lyapunov majorants and the application of the Banach or Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the general feedback synthesis problem, and the pole assignment problem in particular, as well as other basic problems in control theory and linear algebra. (English) |
| Keyword:
|
perturbation analysis |
| Keyword:
|
canonical forms |
| Keyword:
|
feedback synthesis |
| MSC:
|
93B10 |
| MSC:
|
93B28 |
| MSC:
|
93B35 |
| MSC:
|
93B50 |
| MSC:
|
93C05 |
| idZBL:
|
Zbl 1249.93057 |
| idMR:
|
MR2130482 |
| . |
| Date available:
|
2009-09-24T20:06:32Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135636 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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[4] Kantorovich L. V., Akilov G. P.: Functional Analysis in Normed Spaces.Pergamon, New York 1964 Zbl 0127.06104, MR 0213845 |
| Reference:
|
[5] Konstantinov M., Mehrmann, V., Petkov P.: Perturbation Analysis for the Hamiltonian Schur Form.Technical Report 98-17, Fakultät für Mathematik, TU-Chemnitz, Chemnitz 1998 |
| Reference:
|
[6] Konstantinov M. M., Petkov, P. Hr., Christov N. D.: Invariants and canonical forms for linear multivariable systems under the action of orthogonal transformation groups.Kybernetika 17 (1981), 413–424 Zbl 0474.93020, MR 0648213 |
| Reference:
|
[7] Konstantinov M. M., Petkov, P. Hr., Christov N. D.: Nonlocal perturbation analysis of the Schur system of a matrix.SIAM J. Matrix Anal. Appl. 15 (1994), 383–392 Zbl 0798.15010, MR 1266593, 10.1137/S089547989120267X |
| Reference:
|
[8] Konstantinov M. M., Petkov, P. Hr., Christov N. D.: Sensitivity analysis of the feedback synthesis problem.IEEE Trans. Automatic Control 42 (1997), 568–573 Zbl 0878.93020, MR 1442596, 10.1109/9.566671 |
| Reference:
|
[9] Konstantinov M. M., Petkov P. Hr., Christov N. D., Gu D. W., Mehrmann V.: Sensitivity of Lyapunov equations.In: Advances in Intelligent Systems and Computer Science (N. E. Mastorakis, ed.). WSES Press, 1999, pp. 289–292 |
| Reference:
|
[10] Konstantinov M. M., Petkov P. Hr., Gu D. W., Postlethwaite I.: Perturbation Analysis in Finite Dimensional Spaces.Tech. Rep. 96–18, Engineering Department, Leicester University, Leicester 1996 |
| Reference:
|
[11] Konstantinov M. M., Petkov P. Hr., Gu D. W., Postlethwaite I.: Perturbation analysis of orthogonal canonical forms.Linear Algebra Appl. 251 (1997), 267–291 Zbl 0928.93012, MR 1421278 |
| Reference:
|
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| Reference:
|
[13] Petkov P. Hr., Christov N. D., Konstantinov M. M.: A new approach to the perturbation analysis of linear control problems.Preprints 11th IFAC World Congr., Tallin 1990, pp. 311–316 MR 0777050 |
| Reference:
|
[14] Petkov P. Hr., Christov N. D., Konstantinov M. M.: Computational Methods for Linear Control Systems.Prentice–Hall, New York 1991 Zbl 0790.93001 |
| Reference:
|
[15] Petkov P. Hr., Christov N. D., Konstantinov M. M.: Sensitivity of orthogonal canonical forms for single-input systems.In: Proc. 22nd Spring Conference of UBM, Sofia 1992, pp. 66–73 |
| Reference:
|
[16] Petkov P. Hr., Christov N. D., Konstantinov M. M.: Perturbation analysis of orthogonal canonical forms and pole assignment for single-input systems.In: Proc. 2nd European Control Conference, Groningen 1993, pp. 1397–1400 |
| Reference:
|
[17] Petkov P. Hr., Christov N. D., Konstantinov M. M.: Perturbation controllability analysis of linear multivariable systems.Preprints 12th IFAC World Congress, Sydney 1993, pp. 491–494 |
| Reference:
|
[18] Sun J.-G.: On perturbation bounds for the QR factorization.Linear Algebra Appl. 215 (1995), 95–111 Zbl 0816.15010, MR 1317473 |
| Reference:
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[19] Sun J.-G.: Perturbation bounds for the generalized Schur decomposition.SIAM J. Matrix Anal. Appl. 16 (1995), 1328–1340 Zbl 0878.15006, MR 1351473, 10.1137/S0895479892242189 |
| . |
