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Keywords:
dynamic stabilization; nonlinear system; feedback stabilization
dynamic stabilization; nonlinear system; feedback stabilization
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]).
References:
[1] Aeyels D.: Stabilization of a class of non–linear systems by smooth feedback control. Systems Control Lett. 5 (1985), 289–29 DOI 10.1016/0167-6911(85)90024-6 | MR 0791542
[2] Arstein Z.: Stabilization with relaxed controls. Nonlinear Anal. Theory Method Appl. 11 (1983), 1163–1173 MR 0721403
[3] Byrnes C., Isidori A.: New results and examples in nonlinear feedback stabilization. Systems Control Lett. 12 (1989), 437–442 DOI 10.1016/0167-6911(89)90080-7 | MR 1005310 | Zbl 0684.93059
[4] Coron J. M., Praly L.: Adding an integrator for the stabilization problem. Systems Control Lett. 17 (1991), 84–104 DOI 10.1016/0167-6911(91)90034-C | MR 1120754 | Zbl 0747.93072
[5] Dayawansa W. P., Martin C. F.: Asymptotic stabilization of two dimensional real analytic systems. Systems Control Lett. 12 (1989), 205–211 DOI 10.1016/0167-6911(89)90051-0 | MR 0993943 | Zbl 0673.93064
[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 DOI 10.1137/0328070 | MR 1075206 | Zbl 0731.93076
[7] Hermes H.: Asymptotic stabilization of planar systems. Systems Control Lett. 17 (1991), 437–443 DOI 10.1016/0167-6911(91)90083-Q | MR 1138943 | Zbl 0749.93072
[8] Hu X.: Stabilization of planar nonlinear systems by polynomial feedback control. Systems Control Lett. 22 (1994), 177–185 DOI 10.1016/0167-6911(94)90011-6 | MR 1263941
[9] Iggidr A., Sallet G.: Nonlinear stabilization by adding integrators. Kybernetika 30 (1994), 5, 499–506 MR 1314345 | Zbl 0830.93065
[10] Koditschek D. E.: Adaptative techniques for mechanical systems. In: 5th Yale Workshop on Adaptative Systems, 1987, pp. 259-265
[11] Kokotovic P. V., Sussmann H. J.: A positive real condition for global stabilization of nonlinear systems. Systems Control Lett. 13 (1989), 125–133 DOI 10.1016/0167-6911(89)90029-7 | MR 1014238 | Zbl 0684.93066
[12] Lasalle J. P., Lefschetz S.: Stability by Lyapunov Method with Applications. Academic Press, New York 1961 MR 0132876
[13] Outbib R., Sallet G.: Stabilizability of the angular velocity of a rigid body revisited. Systems Control Lett. 18 (1991), 93–98 DOI 10.1016/0167-6911(92)90013-I | MR 1149353
[14] Sontag E. D.: A universal construction of Arstein’s theorem on nonlinear stabilization. Systems Control Lett. 13 (1989), 117–123 DOI 10.1016/0167-6911(89)90028-5 | MR 1014237
[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 DOI 10.1016/0167-6911(89)90052-2 | MR 0993944
[16] Tsinias J.: Sufficient Lyapunov–like conditions for stabilization. Math. Control Signals Systems 18 (1989), 343–357 DOI 10.1007/BF02551276 | MR 1015672 | Zbl 0688.93048
[17] Tsinias J.: A local stabilization theorem for interconnected systems. Systems Control Lett. 18 (1992), 429–434 DOI 10.1016/0167-6911(92)90046-U | MR 1169288 | Zbl 0763.93076
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