| Title:
|
Only a level set of a control Lyapunov function for homogeneous systems (English) |
| Author:
|
Jerbi, Hamadi |
| Author:
|
Kharrat, Thouraya |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
5 |
| Year:
|
2005 |
| Pages:
|
[593]-600 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we generalize Artstein’s theorem and we derive sufficient conditions for stabilization of single-input homogeneous systems by means of an homogeneous feedback law and we treat an application for a bilinear system. (English) |
| Keyword:
|
homogeneous systems |
| Keyword:
|
homogeneous feedbacks |
| Keyword:
|
stabilizability |
| Keyword:
|
sub manifold |
| Keyword:
|
vector field |
| MSC:
|
93D05 |
| MSC:
|
93D15 |
| idZBL:
|
Zbl 1249.93147 |
| idMR:
|
MR2192425 |
| . |
| Date available:
|
2009-09-24T20:11:43Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135680 |
| . |
| Reference:
|
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| Reference:
|
[2] Faubourg L., Pomet J. P.: Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems.ESAIM: Control, Optimization and Calculus of Variations 5 (2000), 293–311 Zbl 0959.93046, MR 1765428, 10.1051/cocv:2000112 |
| Reference:
|
[3] Goodman R. W.: Nilpotent Lie Groups: Structure and Applications to Analysis.(Lecture Notes in Mathematics 562.) Springer–Verlag, Berlin 1976 Zbl 0347.22001, MR 0442149 |
| Reference:
|
[4] Hermes H.: Nilpotent and high-order approximations of vector field systems.SIAM Rev. 33 (1991), 238–264 Zbl 0733.93062, MR 1108590, 10.1137/1033050 |
| Reference:
|
[5] Jerbi H.: A manifold-like characterization of asymptotic stabilizability of homogeneous systems.Systems Control Lett. 45 (2002), 173–178 Zbl 0987.93060, MR 2072233, 10.1016/S0167-6911(01)00172-4 |
| Reference:
|
[6] Kawski M.: Homogeneous stabilizing feedback laws.Control Theory and Advanced Technology 6 (1990), 497–516 MR 1092775 |
| Reference:
|
[7] Closkey R. Mac, Murray M.: Exponential stabilization of driftless nonlinear control systems using homogeneous feedback.IEEE Trans. Automat. Control 42 (1997), 614–628 MR 1454204, 10.1109/9.580865 |
| Reference:
|
[8] Closkey R. Mac, Morin P.: Time-varying homogeneous feedback: design tools for exponential stabilization of systems with drift.Internat. J. Control 71 (1998), 837–869 MR 1658500, 10.1080/002071798221605 |
| Reference:
|
[9] Sontag E. D.: A “universal” construction of Artstein’s Theorem on nonlinear stabilization.Systems Control Lett. 13 (1989) Zbl 0684.93063, MR 1014237, 10.1016/0167-6911(89)90028-5 |
| Reference:
|
[10] Tsinias J.: Stabilization of affine in control nonlinear systems.Nonlinear Anal. 12 (1988), 1238–1296 Zbl 0662.93055, MR 0969506, 10.1016/0362-546X(88)90060-0 |
| Reference:
|
[11] Tsinias J.: Sufficient Lyapunov like conditions for stabilization.Math. Control Signals Systems 2 (1989), 343–357 Zbl 0688.93048, MR 1015672, 10.1007/BF02551276 |
| . |
