| Title:
|
Decoupling normalizing transformations and local stabilization of nonlinear systems (English) |
| Author:
|
Nikitin, S. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
225-248 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given. (English) |
| Keyword:
|
nonlinear system |
| Keyword:
|
stabilization |
| Keyword:
|
center manifold |
| Keyword:
|
normalizing transformation |
| Keyword:
|
smooth feedback |
| MSC:
|
34A34 |
| MSC:
|
34C20 |
| MSC:
|
34C30 |
| MSC:
|
34D05 |
| MSC:
|
34D35 |
| MSC:
|
34D99 |
| MSC:
|
93C10 |
| MSC:
|
93D15 |
| idZBL:
|
Zbl 0863.34013 |
| idMR:
|
MR1419877 |
| DOI:
|
10.21136/MB.1996.125988 |
| . |
| Date available:
|
2009-09-24T21:19:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125988 |
| . |
| Reference:
|
[1] D. Aeyels: Stabilization of a class of nonlinear systems by a smooth feedback contгol.Systems Contгol Lett. 5 (1985), 289-294. MR 0791542 |
| Reference:
|
[2] A. Andreini A. Baccietti G. Stefani: Global stabilizability of homogeneous vector fields of odd degree.Systems Control Lett. 10 (1988), 251-256. MR 0936621, 10.1016/0167-6911(88)90014-X |
| Reference:
|
[3] S. Behtash S. Sastry: Stabilization of nonlinear systems with uncontrollable lineaгization.IEEE Tгans. Automat. Control 33 (1988), 585-590. MR 0940781, 10.1109/9.1259 |
| Reference:
|
[4] J. Carr: Applications of centгe manifold theoгy.Springer, New York, 1981. MR 0635782 |
| Reference:
|
[5] E. Coddington, N. Levinson: Theoгy of ordinary differential equations.McGraw-Hill, New York, 1955. MR 0069338 |
| Reference:
|
[6] M. C. Joshi, R. K. Bose: Some topics in nonlineaг functional analysis.John Wiley and Sons, New York, 1985. MR 0806351 |
| Reference:
|
[7] V. Jurdjevic J. Quin: Controllability and stabilizability.J. Diffeгential Equations 28 (1978), 381-389. MR 0494275, 10.1016/0022-0396(78)90135-3 |
| Reference:
|
[8] A. Kelley: The stable, centeг-stable, centeг, centeг-unstable, unstable manifolds.J. Differential Equations 3 (1967), 546-570. MR 0221044, 10.1016/0022-0396(67)90016-2 |
| Reference:
|
[9] N. Kalouptsidis J. Tsinias: Stability impгovement of nonlinear systems by feedback.IEEE Trans. Automat. Control 29 (1984), 365-367. MR 0742368, 10.1109/TAC.1984.1103518 |
| Reference:
|
[10] E. P. Ryan N. J. Buckingham: On asymptotically stabilizing feedback control of bilinear systems.IEEE Trans. Automat. Control 28 (1983), 863-864. 10.1109/TAC.1983.1103323 |
| Reference:
|
[11] V. I. Zubov: Methods of A.M. Liapunov and their applications.Noordhoff, 1964. MR 0179428 |
| . |
