Title:
|
A reduction principle for global stabilization of nonlinear systems (English) |
Author:
|
Outbib, Rachid |
Author:
|
Sallet, Gauthier |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
34 |
Issue:
|
5 |
Year:
|
1998 |
Pages:
|
[595]-607 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The goal of this paper is to propose new sufficient conditions for dynamic stabilization of nonlinear systems. More precisely, we present a reduction principle for the stabilization of systems that are obtained by adding integrators. This represents a generalization of the well-known lemma on integrators (see for instance [BYIS] or [Tsi1]). (English) |
Keyword:
|
dynamic stabilization |
Keyword:
|
nonlinear system |
Keyword:
|
feedback stabilization |
MSC:
|
93C10 |
MSC:
|
93D15 |
idZBL:
|
Zbl 1274.93229 |
idMR:
|
MR1663748 |
. |
Date available:
|
2009-09-24T19:20:54Z |
Last updated:
|
2015-03-28 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135246 |
. |
Reference:
|
[1] Aeyels D.: Stabilization of a class of non–linear systems by smooth feedback control.Systems Control Lett. 5 (1985), 289–29 MR 0791542, 10.1016/0167-6911(85)90024-6 |
Reference:
|
[2] Arstein Z.: Stabilization with relaxed controls.Nonlinear Anal. Theory Method Appl. 11 (1983), 1163–1173 MR 0721403 |
Reference:
|
[3] Byrnes C., Isidori A.: New results and examples in nonlinear feedback stabilization.Systems Control Lett. 12 (1989), 437–442 Zbl 0684.93059, MR 1005310, 10.1016/0167-6911(89)90080-7 |
Reference:
|
[4] Coron J. M., Praly L.: Adding an integrator for the stabilization problem.Systems Control Lett. 17 (1991), 84–104 Zbl 0747.93072, MR 1120754, 10.1016/0167-6911(91)90034-C |
Reference:
|
[5] Dayawansa W. P., Martin C. F.: Asymptotic stabilization of two dimensional real analytic systems.Systems Control Lett. 12 (1989), 205–211 Zbl 0673.93064, MR 0993943, 10.1016/0167-6911(89)90051-0 |
Reference:
|
[6] Dayawansa W. P., Martin C. F., Knowles G.: Asymptotic stabilization of a class of smooth two dimensional systems.SIAM J. Control Optim. 28 (1990), 1321–1349 Zbl 0731.93076, MR 1075206, 10.1137/0328070 |
Reference:
|
[7] Hermes H.: Asymptotic stabilization of planar systems.Systems Control Lett. 17 (1991), 437–443 Zbl 0749.93072, MR 1138943, 10.1016/0167-6911(91)90083-Q |
Reference:
|
[8] Hu X.: Stabilization of planar nonlinear systems by polynomial feedback control.Systems Control Lett. 22 (1994), 177–185 MR 1263941, 10.1016/0167-6911(94)90011-6 |
Reference:
|
[9] Iggidr A., Sallet G.: Nonlinear stabilization by adding integrators.Kybernetika 30 (1994), 5, 499–506 Zbl 0830.93065, MR 1314345 |
Reference:
|
[10] Koditschek D. E.: Adaptative techniques for mechanical systems.In: 5th Yale Workshop on Adaptative Systems, 1987, pp. 259-265 |
Reference:
|
[11] Kokotovic P. V., Sussmann H. J.: A positive real condition for global stabilization of nonlinear systems.Systems Control Lett. 13 (1989), 125–133 Zbl 0684.93066, MR 1014238, 10.1016/0167-6911(89)90029-7 |
Reference:
|
[12] Lasalle J. P., Lefschetz S.: Stability by Lyapunov Method with Applications.Academic Press, New York 1961 MR 0132876 |
Reference:
|
[13] Outbib R., Sallet G.: Stabilizability of the angular velocity of a rigid body revisited.Systems Control Lett. 18 (1991), 93–98 MR 1149353, 10.1016/0167-6911(92)90013-I |
Reference:
|
[14] Sontag E. D.: A universal construction of Arstein’s theorem on nonlinear stabilization.Systems Control Lett. 13 (1989), 117–123 MR 1014237, 10.1016/0167-6911(89)90028-5 |
Reference:
|
[15] Sontag E. D., Sussmann H. J.: Further comments on the stabilizability on the angular velocity of a rigid body.Systems Control Lett. 12 (1989), 213–217 MR 0993944, 10.1016/0167-6911(89)90052-2 |
Reference:
|
[16] Tsinias J.: Sufficient Lyapunov–like conditions for stabilization.Math. Control Signals Systems 18 (1989), 343–357 Zbl 0688.93048, MR 1015672, 10.1007/BF02551276 |
Reference:
|
[17] Tsinias J.: A local stabilization theorem for interconnected systems.Systems Control Lett. 18 (1992), 429–434 Zbl 0763.93076, MR 1169288, 10.1016/0167-6911(92)90046-U |
. |